منابع مشابه
Spanning eulerian subgraphs in N -locally connected claw-free graphs
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].
متن کاملSpanning eulerian subgraphs in N2-locally connected claw-free graphs
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 connectedN2-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].
متن کاملOdd subgraphs and matchings
Let G be a graph and f : V (G) → {1, 3, 5, . . .}. Then a subgraph H of G is called a (1, f)-odd subgraph if degH(x) ∈ {1, 3, . . . , f(x)} for all x ∈ V (H). If f(x) = 1 for all x ∈ V (G), then a (1, f)-odd subgraph is nothing but a matching. A (1, f)-odd subgraph H of G is said to be maximum if G has no (1, f)-odd subgraph K such that |K| > |H|. We show that (1, f)-odd subgraphs have some pro...
متن کاملEulerian Subgraphs Containing Given Vertices
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.
متن کاملEulerian subgraphs containing given edges
For an integer l¿0, de ne SE(l) to be the family of graphs such that G ∈SE(l) if and only if for any edge subset X ⊆E(G) with |X |6l, G has a spanning eulerian subgraph H with X ⊆E(H). The graphs in SE(0) are known as supereulerian graphs. Let f(l) be the minimum value of k such that every k-edge-connected graph is in SE(l). Jaeger and Catlin independently proved f(0) = 4. We shall determine f(...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90303-8