منابع مشابه
Critical graphs with connected complements
We show that given any vertex x of a k-colour-critical graph G with a connected complement, the graph G − x can be (k − 1)-coloured so that every colour class contains at least 2 vertices. This extends the well-known theorem of Gallai, that a k-colour-critical graph with a connected complement has at least 2k − 1 vertices. Our proof does not use matching theory. It is considerably shorter, conc...
متن کاملDomination critical graphs with respect to relative complements
Let G be a spanning subgraph of Ks,s and let H be the complement of G relative to Ks,s; that is, Ks,s = GtJ)H is a factorization of Ks,s' The graph G is ,,(-critical relative to Ks,s if ,(G) = , and "(( G + e) = , 1 for all e E E(H), where ,(G) denotes the domination number of G. We investigate ,,(-critical graphs for small values of "(. The 2-critical graphs and 3-critical graphs are character...
متن کاملSmooth Surfaces with Non-simply-connected Complements
We give two constructions of surfaces in simply-connected 4-manifolds with non simply-connected complements. One is an iteration of the twisted rim surgery introduced by the first author [7]. We also construct, for any group G satisfying some simple conditions, a simply-connected symplectic manifold containing a symplectic surface whose complement has fundamental group G. In each case, we produ...
متن کاملOn connected (γ, k)-critical graphs
A graph G is said to be (γ, k)-critical if γ(G−S) < γ(G) for any set S of k vertices and domination number γ. Properties of (γ, k)-critical graphs are studied for k ≥ 3. Ways of constructing a (γ, k)-critical graph from smaller (γ, k)-critical graphs are presented.
متن کاملMatching properties in connected domination critical graphs
A dominating set of vertices S of a graph G is connected if the subgraph G[S] is connected. Let c(G) denote the size of any smallest connected dominating set in G. A graph G is k-connected-critical if c(G)= k, but if any edge e ∈ E(Ḡ) is added to G, then c(G+ e) k − 1. This is a variation on the earlier concept of criticality of edge addition with respect to ordinary domination where a graph G ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2003
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(03)00069-8