Onk-Critical Connected Line Graphs
نویسندگان
چکیده
منابع مشابه
Hamiltonian Connected Line Graphs
Thomassen conjectured [8] that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K5−E(C), where C is a cycle of length 4 in K5. In [2], it is shown that every 4-connected line graph without an induced subgraph isomorphic to the hourglass is hamiltonian connected. In this note, we prove that every 3-connected, essentially 4-connected hourglass-free line graph is ...
متن کاملCritical 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 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 ...
متن کاملHamiltonicity of 3-connected line graphs
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Lai et al. conjectured [H. Lai, Y. Shao, H. Wu, J. Zhou, Every 3-connected, essentially 11-connected line graph is Hamiltonian, J. Combin. Theory Ser. B 96 (2006) 571–576] that every 3-connected, essentially 4-connected line graph is Hamiltonian. In this note, we first show that the conjecture posed by Lai et al. is not tru...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1998
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1823