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| In [[graph theory]], '''path coloring''' usually refers to one of two problems:
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| * The problem of coloring a [[multiset|(multi)set]] of [[path (graph theory)|paths]] <math>R</math> in graph <math>G</math>, in such a way that any two paths of <math>R</math> which share an edge in <math>G</math> receive different colors. Set <math>R</math> and graph <math>G</math> are provided at input. This formulation is equivalent to [[Graph coloring|vertex coloring]] the ''conflict graph'' of set <math>R</math>, i.e. a graph with vertex set <math>R</math> and edges connecting all pairs of paths of <math>R</math> which are not edge-disjoint with respect to <math>G</math>.
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| * The problem of coloring (in accordance with the above definition) any chosen [[multiset|(multi)set]] <math>R</math> of paths in <math>G</math>, such that the set of pairs of end-vertices of paths from <math>R</math> is equal to some set or multiset <math>I</math>, called a ''set of requests''. Set <math>I</math> and graph <math>G</math> are provided at input. This problem is a special case of a more general class of graph routing problems, known as [[call scheduling]].
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| In both the above problems, the goal is usually to minimise the number of colors used in the coloring. In different variants of path coloring, <math>G</math> may be a [[simple graph]], [[directed graph|digraph]] or [[multigraph]].
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| ==References==
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| *[http://citeseer.ist.psu.edu/erlebach00complexity.html] ''The Complexity of Path Coloring and Call Scheduling'' by Thomas Erlebach and Klaus Jansen
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| *[http://www.nada.kth.se/~viggo/wwwcompendium/node122.html] ''A compendium of NP optimization problems'' by Viggo Kann (problem: Minimum Path Coloring)
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| [[Category:Graph coloring]]
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Latest revision as of 18:59, 13 March 2014
Andrew Berryhill is what his wife loves to contact him and he completely digs that name. Alaska is where he's always been living. Distributing manufacturing has been his occupation for some time. Doing ballet is some thing she would by no means give up.
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