Graphs with branchwidth at most three

作     者：Bodlaender, HL Thilikos, DM 

作者机构：Univ Utrecht Dept Comp Sci NL-3508 TB Utrecht Netherlands Univ Waterloo Dept Comp Sci DC 2117 Waterloo ON N2L 3G1 Canada 

出 版 物：《JOURNAL OF ALGORITHMS》 (算法杂志)

年 卷 期：1999年第32卷第2期

页      面：167-194页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：ESPRIT  (20244) 

主　　题：graph algorithms branchwidth obstruction set graph minors reduction rule 

摘      要：In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph as a minor. A set of four graphs is shown to be the obstruction set for the class of graphs with branchwidth at most three. Moreover, we give a safe and complete set of reduction rules for the graphs with branchwidth at most three. Using this set, a linear time algorithm is given that verifies if a given graph has branchwidth at most three, and, if so, outputs a minimum width branch decomposition. (C) 1999 Academic Press.