Two conjectures on edge-colouring
Discrete Mathematics - Graph colouring and variations
Discrete Applied Mathematics - Combinatorial Optimization
NP-completeness of edge-colouring some restricted graphs
Discrete Applied Mathematics
A constructive proof of Vizing's Theorem
Information Processing Letters
Minimum proper interval graphs
Discrete Mathematics
A linear-time algorithm for proper interval graph recognition
Information Processing Letters
On edge-colouring indifference graphs
Theoretical Computer Science - Special issue: Latin American theoretical informatics
Total-chromatic number and chromatic index of dually chordal graphs
Information Processing Letters
Chromatic index of graphs with no cycle with a unique chord
Theoretical Computer Science
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The chromatic index problem--finding the minimum number of colours required for colouring the edges of a graph--is still unsolved for indifference graphs, whose vertices can be linearly ordered so that the vertices contained in the same maximal clique are consecutive in this order. We present new positive evidence for the conjecture: every non neighbourhood-overfull indifference graph can be edge coloured with maximum degree colours. Two adjacent vertices are twins if they belong to the same maximal cliques. A graph is reduced if it contains no pair of twin vertices. A graph is overfull if the total number of edges is greater than the product of the maximum degree by ⌈n/2⌉, where n is the number of vertices. We give a structural characterization for neighbourhood-overfull indifference graphs proving that a reduced indifference graph cannot be neighbourhood-overfull. We show that the chromatic index for all reduced indifference graphs is the maximum degree. We present two decomposition methods for edge colouring reduced indifference graphs with maximum degree colours.