منابع مشابه
An s -Hamiltonian Line Graph Problem
For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In [J. Graph Theory, 11 (1987), 399-407], Broersma and Veldman proposed an open problem: For a given positive integer k, determine the value s for which the statement Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected is...
متن کاملOn s-Hamiltonian Line Graphs
For an integer s ≥ 0, a graph G is s-hamiltonian if for any vertex subset S′ ⊆ V (G) with |S′| ≤ s, G − S′ is hamiltonian. It is well known that if a graph G is s-hamiltonian, then G must be (s + 2)-connected. The converse is not true, as there exist arbitrarily highly connected nonhamiltonian graphs. But for line graphs, we prove that when s ≥ 5, a line graph is s-hamiltonian if and only if it...
متن کاملOn s-hamiltonian-connected line graphs
1 A graph G is hamiltonian-connected if any two of its vertices are connected by a Hamilton 2 path (a path including every vertex of G); and G is s-hamiltonian-connected if the deletion 3 of any vertex subset with at most s vertices results in a hamiltonian-connected graph. In this 4 paper, we prove that the line graph of a (t+4)-edge-connected graph is (t+2)-hamiltonian5 connected if and only ...
متن کاملEvery 3-connected, essentially 11-connected line graph is Hamiltonian
Thomassen conjectured that every 4-connected line graph is Hamiltonian. A vertex cut X of G is essential if G−X has at least two non-trivial components. We prove that every 3-connected, essentially 11-connected line graph is Hamiltonian. Using Ryjác̆ek’s line graph closure, it follows that every 3-connected, essentially 11-connected claw-free graph is Hamiltonian. © 2005 Elsevier Inc. All rights...
متن کاملLogical s-t Min-Cut Problem: An Extension to the Classic s-t Min-Cut Problem
Let $G$ be a weighted digraph, $s$ and $t$ be two vertices of $G$, and $t$ is reachable from $s$. The logical $s$-$t$ min-cut (LSTMC) problem states how $t$ can be made unreachable from $s$ by removal of some edges of $G$ where (a) the sum of weights of the removed edges is minimum and (b) all outgoing edges of any vertex of $G$ cannot be removed together. If we ignore the second constraint, ca...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2007
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-007-0727-y