Distance edge-colourings and matchings
نویسندگان
چکیده
منابع مشابه
On distance edge colourings of a cyclic multigraph
We shall use the distance chromatic index defined by the present author in early nineties, cf. [5] or [4] of 1993. The edge distance of two edges in a multigraph M is defined to be their distance in the line graph L(M) of M . Given a positive integer d, define the d+-chromatic index of the multigraph M , denoted by q(d)(M), to be equal to the chromatic number χ of the dth power of the line grap...
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Let k and ` be positive integers. With a graph G, we associate the quantity ck,`(G), the number of k-colorings of the edge set of G with no monochromatic matching of size `. Consider the function ck,` : N −→ N given by ck,`(n) = max {ck,`(G) : |V (G)| = n}, the maximum of ck,`(G) over all graphs G on n vertices. In this paper, we determine ck,`(n) and the corresponding extremal graphs for all l...
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It is shown that the only bipartite distance regular graphs of diameter 3 which are MLDcolourable are the incidence graphs of complementary Hadamard designs.
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We propose the following problem. For some k ≥ 1, a graph G is to be properly edge coloured such that any two adjacent vertices share at most k colours. We call this the k-intersection edge colouring. The minimum number of colours sufficient to guarantee such a colouring is the k-intersection chromatic index and is denoted χk(G). Let fk be defined by fk(∆) = max G:∆(G)=∆ {χk(G)}. We show that f...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.07.001