منابع مشابه
Hamilto-connected derangement graphs on S n
We consider the derangements graph in which the vertices are permutations of f1 : : : ng. Two vertices are joined by an edge if the corresponding permutations diier in every position. The derangements graph is known to be hamil-tonian and it follows from a recent result of Jung that every pair of vertices is joined by a Hamilton path. We use this result to settle an open question, by showing th...
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A graph G is k-Hamilton-connected (k-hamiltonian) if G−X is Hamilton-connected (hamiltonian) for every setX ⊂ V (G) with |X| = k. In the paper, we prove that (i) every 5-connected claw-free graph with minimum degree at least 6 is 1Hamilton-connected, (ii) every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with...
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Let G be a graph and s > 0 be an integer. If, for any function b : V (G) → Z2s+1 satisfying v∈V (G) b(v) ≡ 0 (mod 2s+1), G always has an orientation D such that the net outdegree at every vertex v is congruent to b(v)mod 2s+1, then G is strongly Z2s+1-connected. For a graph G, denote by α(G) the cardinality of a maximum independent set of G. In this paper, we prove that for any integers s, t ...
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A tree is called a k-tree if the maximum degree is at most k. We prove the following theorem, by which a closure concept for spanning k-trees of n-connected graphs can be defined. Let k ≥ 2 and n ≥ 1 be integers, and let u and v be a pair of nonadjacent vertices of an n-connected graph G such that degG(u)+degG(v) ≥ |G|−1−(k−2)n, where |G| denotes the order of G. Then G has a spanning k-tree if ...
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Let G = (V;E) be a graph with vertex set V of size n and edge set E of size m. A vertex v 2 V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hingefree graph. In general, a graph G is k-geodetically connected or k-GC for short if G can tolerate any k 1 vertices failures without increasing the distance among...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1971
ISSN: 0095-8956
DOI: 10.1016/0095-8956(71)90027-x