منابع مشابه
Distance-locally disconnected graphs
For an integer k ≥ 1, we say that a (finite simple undirected) graph G is k-distance-locally disconnected, or simply k-locally disconnected if, for any x ∈ V (G), the set of vertices at distance at least 1 and at most k from x induces in G a disconnected graph. In this paper we study the asymptotic behavior of the number of edges of a k-locally disconnected graph on n vertices. For general grap...
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A graph G is N2-locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryjác̆ek conjectured that every 3-connected N2-locally connected claw-free graph is hamiltonian. This conjecture is proved in this note.
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Let G be a locally compact totally disconnected group. Recall that every neighborhood of 1 in G contains a compact open subgroup. If G is assumed to be compact, then every neighborhood of 1 in G contains a compact open normal subgroup. On the other hand, it follows from properties of Lie groups that the group GL(n,C) has the property that there is some neighborhood of the identity which contain...
متن کاملGallai's conjecture for disconnected graphs
The path number p(G) of a graph G is the minimum number of paths needed to partition the edge set of G. Gallai conjectured that p(G) b n+1 2 c for every connected graph G of order n. Because of the graph consisting of disjoint triangles, the best one could hope for in the disconnected case is p(G) b 2 3 nc. We prove the sharper result that p(G) 1 2 u + b 2 3 gc where u is the number of odd vert...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90551-4