Eulerian subgraphs containing given edges
Eulerian subgraphs containing given edges
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DOI：
10.1016/s0012-365x(00)00070-4
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发表时间：
2001-03
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影响因子：
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通讯作者：
H. Lai
中科院分区：
文献类型：
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作者：
H. Lai
对于整数l <$0，定义SE（l）为图族，使得G∈ SE（l）当且仅当对于任意边子集X <$E（G），|X|图G有一个生成欧拉子图H，其中X ∈ E（H）. SE（0）中的图被称为超欧拉图。设f（l）是使每个k-边连通图都在SE（l）中的k的最小值。Jaeger和Catlin独立证明了f（0）= 4。我们将确定f（l）对所有l ≠ 0的值。本文还讨论了含给定边的欧拉子图的存在性问题，推广了[J. Graph Theory 1（1977）79-84]和[J. Graph Theory 3（1979）91-93]中的结果。
For an integer l⩾ 0, define 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|⩽ l, 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 (l) for all values of l⩾ 0. Another problem concerning the existence of eulerian subgraphs containing given edges is also discussed, and former results in [J. Graph Theory 1 (1977) 79–84] and [J. Graph Theory 3 (1979) 91–93] are extended.