منابع مشابه
Complexity of Generalized Colourings of Chordal Graphs
The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of graphs P1, . . . ,Pk (usually describing some common graph properties), is to decide, for a given graph G, whether the vertex set of G can be partitioned into sets V1, . . . , Vk such that, for each i, the induced subgraph of G on Vi belongs to Pi. It can be seen that GCOL generalizes many natural colouri...
متن کاملComplexity of Generalised Colourings of Chordal Graphs
The graph colouring problem and its derivatives have been notoriously known for their inherent intractability. The difficulty seems to stem from the fact that we want a solution for any given graph, however complex it may be. One of the ways how to overcome this difficulty is to restrict possible inputs to the problem; that is, we ask for a solution only for graphs having some special structure...
متن کاملOn Injective Colourings of Chordal Graphs
We show that one can compute the injective chromatic number of a chordal graph G at least as efficiently as one can compute the chromatic number of (G−B), where B are the bridges of G. In particular, it follows that for strongly chordal graphs and so-called power chordal graphs the injective chromatic number can be determined in polynomial time. Moreover, for chordal graphs in general, we show ...
متن کاملReconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs
A k-colouring of a graph G = (V,E) is a mapping c : V → {1, 2, . . . , k} such that c(u) 6= c(v) whenever uv is an edge. The reconfiguration graph of the k-colourings of G contains as its vertex set the k-colourings of G, and two colourings are joined by an edge if they differ in colour on just one vertex of G. We introduce a class of k-colourable graphs, which we call k-colour-dense graphs. We...
متن کاملChordal Graphs
One can prove the following propositions: (1) For every non zero natural number n holds n − 1 is a natural number and 1 ≤ n. (2) For every odd natural number n holds n − 1 is a natural number and 1 ≤ n. (3) For all odd integers n, m such that n < m holds n ≤ m − 2. (4) For all odd integers n, m such that m < n holds m + 2 ≤ n. (5) For every odd natural number n such that 1 6= n there exists an ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2015.06.005