منابع مشابه
Vertex-Colouring Edge-Weightings
A weighting w of the edges of a graph G induces a colouring of the vertices of G where the colour of vertex v, denoted cv, is ∑ e3v w(e). We show that the edges of every graph that does not contain a component isomorphic to K2 can be weighted from the set {1, . . . , 30} such that in the resulting vertex-colouring of G, for every edge (u, v) of G, cu 6= cv.
متن کاملColouring Polytopic Partitions in �
We consider face-to-face partitions of bounded polytopes into convex polytopes in d for arbitrary d 1 and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed d+1. Partitions of polyhedra in 3 into pentahedra and hexahedra are 5and 6-colourable, respectively. We show that the above numbers are attainable, i.e., in general, th...
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 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 کاملParity vertex colouring of graphs
A parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let χp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds χ(G) ≤ χp(G) ≤ |V (G)| − α(G) + 1, where χ(G) and α(G) are the chromatic number and the independence number of G, re...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2005
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2005.01.001