منابع مشابه
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...
متن کاملFractional Colouring and Hadwiger's Conjecture
This is easy for p 3, true but difficult for p=4 and 5 (in both cases [9, 6] it is equivalent to the four-colour theorem [1, 2, 7]), and open for p 6. It is therefore of interest to examine weakenings of (1.1). If G has no Kp+1 minor, the best upper bound known on its chromatic number is O( p(log p) ). This follows easily from the following theorem of Kostochka [5] or Thomason [8]. Article No. ...
متن کاملEdge colouring by total labellings
We introduce the concept of an edge-colouring total k-labelling. This is a labelling of the vertices and the edges of a graph G with labels 1, 2, . . . , k such that the weights of the edges define a proper edge colouring of G. Here the weight of an edge is the sum of its label and the labels of its two endvertices. We define χt(G) to be the smallest integer k for which G has an edge-colouring ...
متن کاملRecent developments in total colouring
This paper gives a number of recent results concerning total colourings and suggests that recolouring schemes which are somewhat more complex than those currently being considered, need to be developed. Some examples of graphs and colourings which support this assertion are presented. The aim of this paper is firstly to publicise a number of recent results concerning total colourings and second...
متن کاملGraph colouring and the total Betti number
The total Betti number of the independence complex of a graph is an intriguing graph invariant. Kalai and Meshulam have raised the question on its relation to cycles and the chromatic number of a graph, and a recent conjecture on that theme was proved by Bonamy, Charbit and Thomassé. We show an upper bound on the total Betti number in terms of the number of vertex disjoint cycles in a graph. Th...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1990
ISSN: 0166-218X
DOI: 10.1016/0166-218x(90)90073-l