NP-completeness of edge-colouring some restricted graphs

On Edge-colouring Indiierence Graphs on Edge-colouring Indiierence Graphs

Vizing's theorem states that the chromatic index 0 (G) of a graph G is either the maximum degree (G) or (G) + 1. A graph G is called overfull if jE(G)j > (G)bjV (G)j=2c. A suu-cient condition for 0 (G) = (G)+1 is that G contains an overfull subgraph H with (H) = (G). Plantholt proved that this condition is necessary for graphs with a universal vertex. In this paper, we conjecture that, for indi...

The NP-Completeness of Some Edge-Partition Problems

We show that for each fixed n 3 it is NP-complete to determine whether an arbitrary graph can be edge-partitioned into subgraphs isomorphic to the complete graph Kn. The NP-completeness of a number of other edge-partition problems follows immediately.

The NP-completeness of some edge-partitioning problems

Edge-colouring and total-colouring chordless graphs

A graph G is chordless if no cycle in G has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree ∆ ≥ 3 has chromatic index ∆ and total chromatic number ∆+1. The proofs are algorithmic in the sense that we ac...

Edge-colouring of join graphs

A join graph is the complete union of two arbitrary graphs. We give sufficient conditions for a join graph to be 1-factorizable. As a consequence of our results, the Hilton’s Overfull Subgraph Conjecture holds true for several subclasses of join graphs. © 2006 Elsevier B.V. All rights reserved.