Tree decompositions for a class of graphs

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	Tree decompositions for a class of graphs
	Shi, MY; Li, YJ; Tian, F
	1998-07-28
发表期刊	DISCRETE MATHEMATICS
ISSN	0012-365X
卷号	189 期号:1-3 页码:221-232
摘要	For a graph G, if E(G) can be partitioned into several pairwise disjoint sets as {E-1, E-2,..., E-t} such that for any i with 1 less than or equal to i less than or equal to 1, the subgraph induced by E-i in G is a tree of order k(i), then G is said to have a {k(1), k(2),..., k(l)}-tree-decomposition. Ringel [3], and Ouyang and Liu [2] proved that every 2-connected maximal planar bipartite (mpb) graph of order n has a {n - 1, n - 1}-tree-decomposition and {n, n - 2}-tree-decomposition, respectively. Kampen [1] proved that every maximal planar (mp) graph of order n has a {n - 1, n - 1, n - 1}-tree-decomposition. In this paper, we consider the following class of graphs including mpb and mp graphs: A graph G is called a P-k-graph, if \G\ greater than or equal to 3, \E(G)\ = k(\G\ - 2) and \E(H)\ less than or equal to k(\H\ - 2) for any subgraph H of G with \H\ greater than or equal to 3. we prove that (i) for any P-2-graph of order n greater than or equal to 3, it has both a {n, n - 2}-tree-decomposition and a {n - 1, n - 1}-tree-decomposition, and moreover, these two kinds of tree-decompositions can be transformed to each other; (ii) for any P-3-graph of order n greater than or equal to 4, it has three kinds of tree-decompositions: {n, n, n - 3}-, {n, n - 1, n - 2}- and {n - 1, n - 1, n - 1}-tree-decomposition, and moreover, they can be transformed to each other. Since 2-connected mpb graphs are Bz-graphs and mp graphs are P-3-graphs, the results mentioned above from [1-3] are immediately implied by our results. Furthermore, all tree-decompositions above can be found in polynomial time. (C) 1998 Elsevier Science B.V. All rights reserved.
关键词	tree decomposition P-k-graph maximal planar bipartite (mpb) graph maximal planar (mp) graph
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000075397200016
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13950
专题	中国科学院数学与系统科学研究院
作者单位	Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Shi, MY,Li, YJ,Tian, F. Tree decompositions for a class of graphs[J]. DISCRETE MATHEMATICS,1998,189(1-3):221-232.
APA	Shi, MY,Li, YJ,&Tian, F.(1998).Tree decompositions for a class of graphs.DISCRETE MATHEMATICS,189(1-3),221-232.
MLA	Shi, MY,et al."Tree decompositions for a class of graphs".DISCRETE MATHEMATICS 189.1-3(1998):221-232.