منابع مشابه
Locally connected spanning trees on graphs
A locally connected spanning tree of a graph G is a spanning tree T of G such that the set of all neighbors of v in T induces a connected subgraph of G for every v ∈ V (G). The purpose of this paper is to give linear-time algorithms for finding locally connected spanning trees on strongly chordal graphs and proper circular-arc graphs, respectively.
متن کاملSpanning k-Trees of n-Connected Graphs
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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For an integer s > 0 and for u, v ∈ V (G) with u = v, an (s; u, v)-pathsystem of G is a subgraph H of G consisting of s internally disjoint (u, v)-paths, and such an H is called a spanning (s; u, v)-path system if V (H) = V (G). The spanning connectivity κ∗(G) of graph G is the largest integer s such that for any integer k with 1 ≤ k ≤ s and for any u, v ∈ V (G) with u = v, G has a spanning (k;...
متن کاملOn spanning tree packings of highly edge connected graphs
We prove a refinement of the tree packing theorem by Tutte/Nash-Williams for finite graphs. This result is used to obtain a similar result for end faithful spanning tree packings in certain infinite graphs and consequently to establish a sufficient Hamiltonicity condition for the line graphs of such graphs.
متن کاملSpanning trails in essentially 4-edge-connected graphs
A connected graphG is essentially 4-edge-connected if for any edge cut X ofGwith |X | < 4, either G − X is connected or at most one component of G − X has edges. In this paper, we introduce a reductionmethod and investigate the existence of spanning trails in essentially 4-edge-connected graphs. As an application, we prove that if G is 4-edge-connected, then for any edge subset X0 ⊆ E(G) with |...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.03.072