Steinberg-like theorems for backbone colouring
نویسندگان
چکیده
منابع مشابه
List circular backbone colouring
A natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge. In the q-backbone colouring problem, these minimum distances are either q or 1, depending on whether or not the edge is in the backbone. In this paper we consider the list version o...
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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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Given a graph G and a spanning subgraph T of G, a backbone k-colouring for (G,T ) is a mapping c : V (G)→ {1, . . . ,k} such that |c(u)− c(v)| ≥ 2 for every edge uv ∈ E(T ) and |c(u)− c(v)| ≥ 1 for every edge uv ∈ E(G) \E(T ). The backbone chromatic number BBC(G,T ) is the smallest integer k such that there exists a backbone k-colouring of (G,T ). In 2007, Broersma et al. [2] conjectured that B...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2015
ISSN: 1571-0653
DOI: 10.1016/j.endm.2015.07.038