منابع مشابه
Colouring graphs with bounded generalized colouring number
Given a graph G and a positive integer p, χp(G) is the minimum number of colours needed to colour the vertices of G so that for any i ≤ p, any subgraph H of G of tree-depth i gets at least i colours. This paper proves an upper bound for χp(G) in terms of the k-colouring number colk(G) of G for k = 2p−2. Conversely, for each integer k, we also prove an upper bound for colk(G) in terms of χk+2(G)...
متن کاملEdge-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...
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 کاملBiclique-colouring verification complexity and biclique-colouring power graphs
Biclique-colouring is a colouring of the vertices of a graph in such a way that no maximal complete bipartite subgraph with at least one edge is monochromatic. We show that it is coNP-complete to check whether a given function that associates a colour to each vertex is a bicliquecolouring, a result that justifies the search for structured classes where the biclique-colouring problem could be ef...
متن کاملH-colouring bipartite graphs
For graphs G and H, an H-colouring of G (or homomorphism from G to H) is a function from the vertices of G to the vertices of H that preserves adjacency. H-colourings generalize such graph theory notions as proper colourings and independent sets. For a given H, k ∈ V (H) and G we consider the proportion of vertices of G that get mapped to k in a uniformly chosen H-colouring of G. Our main resul...
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ژورنال
عنوان ژورنال: Nature
سال: 1897
ISSN: 0028-0836,1476-4687
DOI: 10.1038/056566b0