General and acyclic sum-list-colouring of graphs
نویسندگان
چکیده
منابع مشابه
Acyclic colouring of graphs
A vertex colouring of a graph G is called acyclic if no two adjacent vertices have the same colour and there is no two-coloured cycle in G. The acyclic chromatic number of G, denoted by A(G), is the least number of colours in an acyclic colouring of G. We show that if G has maximum degree d then A(G) = O(d 4 3 ) as d → ∞. This settles a problem of Erdős who conjectured, in 1976, that A(G) = o(d...
متن کاملGame List Colouring of Graphs
We consider the two-player game defined as follows. Let (G,L) be a graph G with a list assignment L on its vertices. The two players, Alice and Bob, play alternately on G, Alice having the first move. Alice’s goal is to provide an L-colouring of G and Bob’s goal is to prevent her from doing so. A move consists in choosing an uncoloured vertex v and assigning it a colour from the set L(v). Adjac...
متن کاملList backbone colouring of graphs
Suppose G is a graph and H is a subgraph of G. Let L be a mapping that assigns to each vertex v of G a set L(v) of positive integers. We say (G,H) is backbone L-colourable if there is a proper vertex colouring c of G such that c(v) ∈ L(v) for all v ∈ V , and |c(u) − c(v)| > 2 for every edge uv in H . We say (G,H) is backbone k-choosable if (G,H) is backbone Lcolourable for any list assignment L...
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3-list colouring is an NP-complete decision problem. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving 3-list colouring on permutation graphs.
متن کاملAcyclic colouring of 1-planar graphs
A graph is 1-planar if it can be drawn on the plane in such a way that every edge crosses at most one other edge. We prove that the acyclic chromatic number of every 1-planar graph is at most 20.
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ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2016
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm161011026d