منابع مشابه
Spanning subgraph with Eulerian components
A graph is k-supereulerian if it has a spanning even subgraph with at most k components. We show that if G is a connected graph and G is the (collapsible) reduction of G, then G is k-supereulerian if and only if G is k-supereulerian. This extends Catlin’s reduction theorem in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44]. For a graph G, l...
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A vertex set S ⊆ V (G) is k-weak-edge-connected if for every C ⊂ S and x ∈ S−C there are min{k, |C|} edge-disjoint (x,C)-paths in G. For a graph G and a k-weakedge-connected vertex set S ⊂ V (G) with k ≥ 3 and 4 ≤ |S| ≤ 2k, we show that G has an eulerian subgraph containing all vertices in S.
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A graph G is Nm-locally connected if for every vertex v in G, the vertices not equal to v and with distance at most m to v induce a connected subgraph in G. We show that both connected N2-locally connected claw-free graph and 3-edge-connected N3-locally connected claw-free graph have connected even [2, 4]-factors, which settle a conjecture by Li in [6].
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.11.003