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JGT
2007
13 years 4 months ago
2007
It is known that for every integer k ≥ 4, each k-map graph with n vertices has at most kn − 2k edges. Previously, it was open whether this bound is tight or not. We show that ...
JGT
2007
13 years 4 months ago
2007
We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved...
JGT
2007
13 years 4 months ago
2007
A cyclic colouring of a plane graph is a vertex colouring such that vertices incident with the same face have distinct colours. The minimum number of colours in a cyclic colouring...
JGT
2007
13 years 4 months ago
2007
We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a backbone color...
JGT
2007
13 years 4 months ago
2007
: Let G be a graph with maximum degree d ≥ 3 and ω(G) ≤ d, where ω(G) is the clique number of the graph G. Let p1 and p2 be two positive integers such that d = p1 + p2. In th...