McCuaig, William2009-08-202009-08-2019882009-08-20http://hdl.handle.net/1828/1558An 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.entechnical reports (mathematics and statistics)Technical ReportDepartment of Mathematics and Statistics