Colouring graphs with no odd holes
نویسندگان
چکیده
An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyárfás made the conjecture that for all t there exists n such that every graph with no Kt subgraph and no odd hole is n-colourable. We prove this conjecture.
منابع مشابه
A greedy method for edge-colouring odd maximum degree doubly chordal graphs
We describe a greedy vertex colouring method which can be used to colour optimally the edge set of certain chordal graphs. This new heuristic yields an exact edge-colouring algorithm for odd maximumdegree doubly chordal graphs. This method shows that any such graph G can be edge-coloured with maximum degree (G) colours, i.e., all these graphs are Class 1. In addition, this method gives a simple...
متن کاملINSTITUTO DE COMPUTAÇÃO UNIVERSIDADE ESTADUAL DE CAMPINAS Clique-colouring of some circulant graphs
A clique-colouring of a graph G is a colouring of the vertices of G so that no maximal clique of size at least two is monochromatic. The clique-hypergraph, H(G), of a graph G has V (G) as its set of vertices and the maximal cliques of G as its hyperedges. A vertex-colouring of H(G) is a clique-colouring of G. Determining the clique-chromatic number, the least number of colours for which a graph...
متن کاملOn the Edge-colouring of Split Graphs on the Edge-colouring of Split Graphs
We consider the following question: can split graphs with odd maximum degree be edge-coloured with maximum degree colours? We show that any odd maximum degree split graph can be transformed into a special split graph. For this special split graph, we were able to solve the question, in case the graph has a quasi-universal vertex.
متن کاملChromatic index of graphs with no cycle with a unique chord
The class C of graphs that do not contain a cycle with a unique chord was recently studied by Trotignon and Vušković [26], who proved strong structure results for these graphs. In the present paper we investigate how these structure results can be applied to solve the edgecolouring problem in the class. We give computational complexity results for the edge-colouring problem restricted to C and ...
متن کاملOn 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014