Ordered colourings of line graphs of trees

Date

2009-08-20T23:12:43Z

Authors

McCuaig, William

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Abstract

An ordered colouring of a graph G is a function c from V(G) into the positive integers such that for every pair of vertices u and v and for every (u,v)-path P, if c(u)=c(v) then there exists an internal vertex x of P with c(u)<c(x). An ordered colouring of G is minimal if the largest integer in the range is minimal. We give a polynomial algorithm for finding a minimal ordered colouring of a line graph of a tree. We then extend the algorithm to a larger class of graphs.

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