Maximum graphs non-Hamiltonian-connected from a vertex
نویسندگان
چکیده
منابع مشابه
A Survey of Graphs Hamiltonian - Connected from a Vertex
A graph G is called hamiltonian-<:onnectedfrom a vertex v ifa hamiltonian path exists from v to every other vertex w ~ v. We present a survey of the main results known about such graphs, including a section on graphs uniquely hamiltonian-connected from a venex and a section on the computational complexity ofdetermining whether a given graph is hamiltonian-<:onnectedfrom a venex or uniquely hami...
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Given a graph G and a positive integer k, denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k. A graph G is called pseudo-k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo-k Hamiltonian-connec...
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For a simple graph G, let NC D(G) = min{|N (u) ∪ N (v)| + d(w) : u, v, w ∈ V (G), uv 6∈ E(G), wv or wu 6∈ E(G)}. In this paper, we prove that if NC D(G) ≥ |V (G)|, then either G is Hamiltonian-connected, or G belongs to a well-characterized class of graphs. The former results by Dirac, Ore and Faudree et al. are extended. c © 2008 Published by Elsevier Ltd
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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 ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1984
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500005462