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	关于2-边连通3正则图荫度的一个注（英文）; A Note on Arboricity of 2-edge-connected Cubic Graphs
	郝荣霞 ; 赖虹建 ; 刘浩洋
	2015
关键词	边连通度 诱导森林 荫度 edge-connectivity induced forest arboricity
英文摘要	图G的点荫度a(G)是G的使得每个子集诱导一个森林的顶点划分中子集的最少个数.我们熟知对任何平面图G,a(G)≤3,且对任何直径最大是2的平面图有a(G)≤2.文献[European J.Combin.,2008,29(4):1064-1075]中给出下列猜想:任何没有3-圈的平面图都有一个顶点的划分(V_1,V_2)使得V_1是独立集,V_2诱导一个森林.本文证明了任何2-边连通上可嵌入的3-正则图G(G≠K_4)都有一个顶点的划分(V_1,V_2)使得V_1是独立集,V_2诱导一个森林.; The vertex-arboricity a(G) of a graph G is the minimum number of subsets into which the set of vertices of G can be partitioned so that each subset induces a forest. It is well known that a(G) ≤ 3 for any planar graph G, and that a(G) ≤ 2 for any planar graph G of diameter at most 2. The conjecture that every planar graph G without 3-cycles has a vertex partition （V_1， V_2） such that V_1 is an independent set and V_2 induces a forest was given in [European J. Combin., 2008,29(4): 1064-1075]. In this paper, we prove that a 2-edge-connected cubic graph which satisfies some condition has this partition. As a corollary, we get the result that every up-embeddable 2-edge-connected cubic graph G (G ≠ K_4) has a vertex partition （V_1， V_2） such that V_1 is an independent set and V_2 induces a forest.; 中国科技核心期刊(ISTIC); 中国科学引文数据库(CSCD); 06; 865-870; 44
语种	中文
出处	CSCD ; 知网
出版者	数学进展
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/432439]
专题	数学科学学院
推荐引用方式 GB/T 7714	郝荣霞,赖虹建,刘浩洋. 关于2-边连通3正则图荫度的一个注（英文）, A Note on Arboricity of 2-edge-connected Cubic Graphs. 2015-01-01.

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