en>Trappist the monk: /* References */Fix CS1 deprecated coauthor parameter errors; using AWB

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References: Fix CS1 deprecated coauthor parameter errors; using AWB

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	~~{{Infobox graph~~
	~~\| name = Bull graph~~
	~~\| image = [[Image:Bull graph.circo.svg\|170px]]~~
	~~\| image_caption = The Bull graph~~
	~~\| namesake =~~
	~~\| vertices = 5~~
	~~\| edges = 5~~
	~~\| automorphisms = 2 ('''Z'''/2'''Z''')~~
	~~\| diameter = 3~~
	~~\| girth = 3~~
	~~\| radius = 2~~
	~~\| chromatic_number = 3~~
	~~\| chromatic_index = 3~~
	~~\| properties = [[planar graph\|Planar]]<br>[[unit distance graph\|Unit distance]]~~
	}}

	In the [[mathematics\|mathematical]] field of [[graph theory]], the '''bull graph''' is a [[planar graph\|planar]] [[undirected graph]] with 5 vertices and 5 edges, in the form of a triangle with two disjoint pendant edges.<ref>{{MathWorld\|urlname=BullGraph\|title=Bull Graph}}</ref>

	It ~~has [[chromatic number]] 3~~, ~~[[chromatic index]] 3~~, ~~radius 2~~, ~~diameter 3~~ and ~~[[girth (graph theory~~)~~\|girth]] 3~~. ~~It is also~~ a ~~1-[[k-vertex-connected graph\|vertex-connected graph]]~~ and ~~a 1-[[k-edge-connected graph\|edge-connected graph]]~~.		It was the end of June. The weather was very hot but the Boss had prepared a full day`�s sales training in the conference room.<br>After a delicious meal, the sales people went back to the afternoon session. The boss did a short resume of the technical elements of the new products shown that morning. He had always been convinced that a mastery of knowing the technical features of a product was the basis of all long term achievement in sales.<br><br>But, in spite of their efforts, they battled to keep their eyes open. And after that he handed it to me. (I said to myself that this was the most tough time slot of the day, and the boss let me get it! How in the world am I going to pull these professionals out of their wish to take a nap?) Here is what I shared: �How many of you had an appointment with a customer, but who left only a couple of minutes before you arrived?<br><br>� Raise your hands please. � Who has had a consultation with a client, who listened to all you had to say extremely politely however when you started to close, he says: �I�m sorry but I've no more budget for this year. I can�t buy now�. All the hands were raised. How did you fe<br>?
			Mike answered, � I just did an hour�s drive to go and see him. He could have told me on the phone. I'd have been better off going fishing that afternoon! �. All the others were laughing. I let them share some of their negative experiences concerning the sales they were counting on, but didn�t come to <br><br>.

	~~==Bull-free graphs==~~		� That is completely frustrating, isn�t it? But the worst part is what we say: �The day is off to a bad start or is finishing like it started�. We begin worrying. �How will reach my objectives for the month? �Frankly, we do not feel sure of ourselves or our products a<br>more.
	~~A graph~~ is ~~bull-free if~~ it ~~has no bull as an [[induced subgraph]]~~. ~~The [[triangle-free graph]]s are bull-free graphs, since every bull contains a triangle~~. ~~The [[strong perfect graph theorem]] was proven~~ for ~~bull-free graphs long before its proof for general graphs~~,<~~ref~~>~~{{citation\|last1=Chvátal\|first1=V~~.~~\|author1-link=Václav Chvátal\|last2=Sbihi\|first2=N~~.~~\|title=Bull-free Berge graphs are perfect\|journal=Graphs and Combinatorics\|volume=3\|year=1987\|pages=127–139\|issue=1\|doi=10~~.~~1007~~/~~BF01788536}}.<~~/~~ref> and a [[polynomial time]~~] ~~recognition algorithm for Bull-free perfect graphs is known~~.~~<ref>{{citation\|last1=Reed\|first1=B~~.~~\|author1-link=Bruce Reed (mathematician~~)~~\|last2=Sbihi\|first2=N.\|title=Recognizing bull-free~~ perfect ~~graphs\|journal=Graphs~~ and ~~Combinatorics\|volume=11\|year=1995\|pages=171–178\|issue=2\|doi=10~~.~~1007~~/~~BF01929485}}.~~<~~/ref~~>		And each �No� or client who is absent, [http://Www.Wonderhowto.com/search/weakens/ weakens] our drive to continue. And in that case, we do not try as hard to close the next possible sale that comes up. � A) My very best sale ever Who would be interested by a perfect method to withstand all negative events of the day and never miss a [http://tinyurl.com/kecvhhb ugg boo<br><br>ale]?

	~~[[Maria Chudnovsky]] and Shmuel Safra have studied bull-free graphs~~ more ~~generally~~, ~~showing that any such graph must have either a large [[clique~~ (~~graph theory)\|clique]] or a large [[independent set]]~~,~~<ref>{{citation\|last1=Chudnovsky\|first1=M.\|author1-link=Maria Chudnovsky\|last2=Safra\|first2=S.\|title=The Erdős–Hajnal conjecture for bull-free graphs\|journal=Journal~~ of ~~Combinatorial Theory~~, ~~Series B\|volume=98\|issue=6\|year=2008\|pages=1301–1310\|doi=10~~.~~1016/j.jctb.2008.02.005\|url=http://www.columbia.edu/~mc2775/EHbullfree.ps}}~~.<~~/ref~~> ~~and developing a general structure theory for these graphs.~~<~~ref~~>~~{{citation\|last=Chudnovsky\|first=M~~.\|authorlink=Maria Chudnovsky\|year=2008\|title=The structure of bull-free graphs. I. Three-edge paths with centers and anticenters\|url=http://www.columbia.edu/~mc2775/bulls1.pdf}}.</ref><ref>{{citation\|last=Chudnovsky\|first=M.\|authorlink=Maria Chudnovsky\|year=2008\|title=The structure of bull-free graphs. II. Elementary trigraphs\|url=http://www.columbia.edu/~mc2775/bulls2.pdf}}.</ref><ref>{{citation\|last=Chudnovsky\|first=M.\|authorlink=Maria Chudnovsky\|year=2008\|title=The structure of bull-free graphs. III. Global structure\|url=http://www.columbia.edu/~mc2775/bulls3.pdf}}.</ref>		All of a sudden no one was tired any more. Well, according to Behavioral specialists, most people cannot think about two things at the same time. (Except you, of course, Mike.) Laughter. So it is most likely better if we direct our thoughts in the direction that will create the mo<br><br>ales.

	~~==Chromatic and characteristic polynomial==~~		What do you think? We've the tendency to create a series of events based on inadequate data. I did 4 sales demonstrations with out a [http://tinyurl.com/kecvhhb ugg boots sale] so the day is off to a poor start. Other days, right from the starting of the day, we did 3 demonstrations, three sales! For those days, I do not need to explain how to go <br><br>t it.
	~~[[File:Chromatically equivalent graphs~~.~~svg\|thumb\|left\|200px\|<center>The three graphs~~ with a [~~[chromatic polynomial~~]~~] equal~~ to <~~math~~>~~(x-2)(x-1)^3x~~<~~/math~~>.~~</center>]]~~

	~~The [[chromatic polynomial]]~~ of the ~~bull graph is~~ <~~math~~>(x-~~2)(x-1)^3x</math>~~. ~~Two other graphs are chromatically equivalent~~ to the ~~bull graph~~.		Smile. But for the days where we're struggling, what should we do? Does this interest you? Yes! � I have a lot of them, so I certainly wish to know! � stated Mike. You know that although I�m a Sales Director, I�m also selling on the field every day. I wouldn�t wish to tell you anything that I haven�t gone thro<br>h myself.
			So I�m going to tell you about my best-ever sales day. I�ll always remember the evening of the 16th of January 1988. My oldest boy who was about 11 at the time ran to meet me with the important question for a family who lives from sales. � Daddy, just how much did you<br><br>l today?

	~~Its [[characteristic polynomial]]~~ is <~~math~~>~~-x(x^2-x-3)(x^2+x-1)~~<~~/math~~>.		� That way he could proudly bring this info to his mother who was cooking in the kitchen. A great day, at that time, was 5000 French francs. � Guess, � I stated to him. He knew that 5000 was good. Five thousand. More! 10000 ! More ! 20000 ? More ! He began<br>etting giddy.
			He ran to see his little brother. It is more than 20000! His little brother continued the bidding. 30000. More! 40000? More! My turn, said Nathan. 50000 ? More! Mommy, Mommy, It�s more than 50000 ! Is that true ? She immediately came, carrying our infant. 60000 ? Nat cont<br><br>d : 70000 ?

	~~Its [[Tutte polynomial]] is~~ <~~math~~>~~x^4+x^3+x^2y~~<~~/math~~>.		More ! Eighty-thousand ??? More ! He breathed deeply and closed his eyes. 100000 ? A little less than 93000 in three sales. The client that bought 84000 francs from me between 10 and 12 said I would be paid in 14 days� time! At that time, I was in big finan<br><br> difficulty.
	~~{{-}}~~

	~~== References ==~~		I completely needed the money to come in so I could pay my bills. (I had about 30% pure profit on those sales!) Following three weeks our accountant said that the money was in and that he could give us a bank check if we needed an advance in commissions! We asked him if we could come by today away simply because our banker was<br><br>eatening us.
	~~{{reflist}}~~

	[[~~Category~~:~~Individual graphs~~]]		All right, come. There was an hour�s drive between our company and our bank. Our boys wanted completely to come with us. On the way back there was a MacDonald�s Restaurant. We stopped there to celebrate. And we digested it very well (the money I mean). The sales persons gave this story a long applause simply because they have<br>ll been there.
	[~~[Category~~:~~Planar graphs]~~]		They've all had the large unexpected sale that saved an otherwise horrible month. So I continued. Who has already had a great sale like that? All the hands had been raised, even Mike�s. Alright, this really is what I recommend. Write down on this 3 by 5 Bristol card and describe your<br><br>t sale ever.

			Take your time. The idea would be to describe your emotional state before the sale, what you felt when you saw it was going to be a mega sale, and detail the emotions that you had when you told your family and friends about it (or even your boss!). There was a �religious� silence as each one savored some of the memorable moments of their profession. Even the boss, sitting at the back of the room <br><br>writing away!

			B) OK, tell us your story, and share with us the feelings you felt! Following some time, I asked who wished to share their best-ever [http://tinyurl.com/kecvhhb ugg boots sale]. Jean-Marc told us how a transport company that he had prospected months before with out success contacted our service and invited him to ask fo<br>an appointment.
			He said to himself that he might do a great day�s sale, perhaps 5-6000 euros. He was far under! The client wanted to restructure all his archives and be able to find all his documents in 2 seconds. It just happened to be that we had a numeric filing system with folders manufactured in polypropylene in different sizes adapted to his profession. In fact, the client bought 40000� worth of this innovative filing system that Jean-Marc so<br><br>hat very day!

			He told us that the same client, one month later sent a second order of the same quantity for another department! Mohamed told us how he drove by a company for the last 10 years hidden in a curve of the road. He truly sensed that this looked like an interesting [http://www.Wonderhowto.com/search/pro<br>ect/ prospect].
			But there was no way of stopping and he couldn�t see exactly where the entry road was. But one month of December, times were so difficult, and the sales had been so low, that he said he had nothing to lose to spend some time to attempt to find the entrance<br><br>this company.

			He was warmly welcomed by the potential client and the he purchased every thing Jean-Marc had to sell. � You know, I don�t have time to go to town to get what I need. It doesn�t bother me to pay a bit more, if somebody comes to visit me. But it�s been ten ye<br>s that I�m here.
			I've ever seen a single salesman! � My colleague waived ten years of sales because he didn�t follow his intuition! This totally unexpected sale was equivalent to 3 weeks sales in normal times and it permitted him to appreciate Christmas time with his family. I recommended that they would put themselves two-by-two to share their best-ever sa<br><br>ith each other!

			(It is much better than sharing your latest disaster, isn�t it?) No one saw the time fly. We were all on another planet! Even Mike (for once) had a great sales adventure to tell the others. Conclusion i) An infallible method to resist negative events durin<br>your selling day.
			ii) How never again miss a [http://tinyurl.com/kecvhhb ugg boots sale] and always be on top of things. iii) Describe your best sale, write it down, and think of your feelings before and after. iv) Even when you feel depressed, you may be only a minute away from your best sale ever. What do yo<br><br>ink about that?

			v) Write several of these stories to encourage you throughout difficult moments. Why not describe your best weekly [http://tinyurl.com/kecvhhb ugg boots sale]? If you do not encourage your self, who will? AA/01/13 Andre Amsing is the writer of the articles on website and if you would want to find out the very best online profit model that John Chow shares in his new e book �The Ultimate Online Profit Model click right here: website top salespersons have the ability to resist negative influences

en>Leszek Jańczuk: /* Description */ link

2013-10-01T10:59:48Z

Description: link

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	I'~~m Aracelis~~ and ~~I live~~ in ~~Garching~~. <br>~~I'm interested in Biological Sciences~~, ~~Target Shooting~~ and ~~Chinese art~~. ~~I like travelling~~ and ~~watching 2 Broke Girls~~.<br><br>~~Here~~ is ~~my web page~~ - [http://~~tinyurl~~.~~com~~/~~kecvhhb ugg boots sale~~]		{{Infobox graph
			\| name = Bull graph
			\| image = [[Image:Bull graph.circo.svg\|170px]]
			\| image_caption = The Bull graph
			\| namesake =
			\| vertices = 5
			\| edges = 5
			\| automorphisms = 2 ('''Z'''/2'''Z''')
			\| diameter = 3
			\| girth = 3
			\| radius = 2
			\| chromatic_number = 3
			\| chromatic_index = 3
			\| properties = [[planar graph\|Planar]]<br>[[unit distance graph\|Unit distance]]
			}}

			In the [[mathematics\|mathematical]] field of [[graph theory]], the '''bull graph''' is a [[planar graph\|planar]] [[undirected graph]] with 5 vertices and 5 edges, in the form of a triangle with two disjoint pendant edges.<ref>{{MathWorld\|urlname=BullGraph\|title=Bull Graph}}</ref>

			It has [[chromatic number]] 3, [[chromatic index]] 3, radius 2, diameter 3 and [[girth (graph theory)\|girth]] 3. It is also a 1-[[k-vertex-connected graph\|vertex-connected graph]] and a 1-[[k-edge-connected graph\|edge-connected graph]].

			==Bull-free graphs==
			A graph is bull-free if it has no bull as an [[induced subgraph]]. The [[triangle-free graph]]s are bull-free graphs, since every bull contains a triangle. The [[strong perfect graph theorem]] was proven for bull-free graphs long before its proof for general graphs,<ref>{{citation\|last1=Chvátal\|first1=V.\|author1-link=Václav Chvátal\|last2=Sbihi\|first2=N.\|title=Bull-free Berge graphs are perfect\|journal=Graphs and Combinatorics\|volume=3\|year=1987\|pages=127–139\|issue=1\|doi=10.1007/BF01788536}}.</ref> and a [[polynomial time]] recognition algorithm for Bull-free perfect graphs is known.<ref>{{citation\|last1=Reed\|first1=B.\|author1-link=Bruce Reed (mathematician)\|last2=Sbihi\|first2=N.\|title=Recognizing bull-free perfect graphs\|journal=Graphs and Combinatorics\|volume=11\|year=1995\|pages=171–178\|issue=2\|doi=10.1007/BF01929485}}.</ref>

			[[Maria Chudnovsky]] and Shmuel Safra have studied bull-free graphs more generally, showing that any such graph must have either a large [[clique (graph theory)\|clique]] or a large [[independent set]],<ref>{{citation\|last1=Chudnovsky\|first1=M.\|author1-link=Maria Chudnovsky\|last2=Safra\|first2=S.\|title=The Erdős–Hajnal conjecture for bull-free graphs\|journal=Journal of Combinatorial Theory, Series B\|volume=98\|issue=6\|year=2008\|pages=1301–1310\|doi=10.1016/j.jctb.2008.02.005\|url=http://www.columbia.edu/~mc2775/EHbullfree.ps}}.</ref> and developing a general structure theory for these graphs.<ref>{{citation\|last=Chudnovsky\|first=M.\|authorlink=Maria Chudnovsky\|year=2008\|title=The structure of bull-free graphs. I. Three-edge paths with centers and anticenters\|url=http://www.columbia.edu/~mc2775/bulls1.pdf}}.</ref><ref>{{citation\|last=Chudnovsky\|first=M.\|authorlink=Maria Chudnovsky\|year=2008\|title=The structure of bull-free graphs. II. Elementary trigraphs\|url=http://www.columbia.edu/~mc2775/bulls2.pdf}}.</ref><ref>{{citation\|last=Chudnovsky\|first=M.\|authorlink=Maria Chudnovsky\|year=2008\|title=The structure of bull-free graphs. III. Global structure\|url=http://www.columbia.edu/~mc2775/bulls3.pdf}}.</ref>

			==Chromatic and characteristic polynomial==
			[[File:Chromatically equivalent graphs.svg\|thumb\|left\|200px\|<center>The three graphs with a [[chromatic polynomial]] equal to <math>(x-2)(x-1)^3x</math>.</center>]]

			The [[chromatic polynomial]] of the bull graph is <math>(x-2)(x-1)^3x</math>. Two other graphs are chromatically equivalent to the bull graph.

			Its [[characteristic polynomial]] is <math>-x(x^2-x-3)(x^2+x-1)</math>.

			Its [[Tutte polynomial]] is <math>x^4+x^3+x^2y</math>.
			{{-}}

			== References ==
			{{reflist}}

			[[Category:Individual graphs]]
			[[Category:Planar graphs]]

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I'm Aracelis and I live in Garching. <br>I'm interested in Biological Sciences, Target Shooting and Chinese art. I like travelling and watching 2 Broke Girls.<br><br>Here is my web page - [http://tinyurl.com/kecvhhb ugg boots sale]

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en>Trappist the monk: /* References */Fix CS1 deprecated coauthor parameter errors; using AWB

en>Leszek Jańczuk: /* Description */ link

en>Helpful Pixie Bot: ISBNs (Build KE)