منابع مشابه
H-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...
متن کامل25 Pretty graph colouring problems
Even if there is nothing more to say about the 4-colour-problem, there are very many easily formulated unsolved graph colouring problems left. We have selected a list of 25 pretty problems. If a class of graphs is closed under minors (deletions and contractions), is the maximum chromatic number of graphs in the class equal to the largest order of a complete graph in the class? Assume that all v...
متن کاملSurjective H-Colouring over Reflexive Digraphs
The Surjective H-Colouring problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce endo-triviality, the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theo...
متن کاملOn colouring (2P2, H)-free and (P5, H)-free graphs
The Colouring problem asks whether the vertices of a graph can be coloured with at most $k$ colours for a given integer $k$ in such a way that no two adjacent vertices receive the same colour. A graph is $(H_1,H_2)$-free if it has no induced subgraph isomorphic to $H_1$ or $H_2$. A connected graph $H_1$ is almost classified if Colouring on $(H_1,H_2)$-free graphs is known to be polynomial-time ...
متن کاملSome colouring problems for unit-quadrance graphs
The quadrance between two points A1 = (x1, y1) and A2 = (x2, y2) is the number Q(A1, A2) = (x1 − x2) + (y1 − y2). Let q be an odd prime power and Fq be the finite field with q elements. The unit-quadrance graph Dq has the vertex set F 2 q , and X,Y ∈ F 2 q are adjacent if and only if Q(A1, A2) = 1. In this paper, we study some colouring problems for the unit-quadrance graph Dq and discuss some ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1995
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00189-p