On the Eternal Vertex Cover Numbers of Generalized Trees

• ARAKI Hisashi

  Department of Computer Science and Engineering, Toyohashi University of Technology

• FUJITO Toshihiro

  Department of Computer Science and Engineering, Toyohashi University of Technology

• INOUE Shota

  Department of Computer Science and Engineering, Toyohashi University of Technology

抄録

Suppose one of the edges is attacked in a graph G, where some number of guards are placed on some of its vertices. If a guard is placed on one of the end-vertices of the attacked edge, she can defend such an attack to protect G by passing over the edge. For each of such attacks, every guard is allowed either to move to a neighboring vertex, or to stay at where she is. The eternal vertex cover number τ^∞(G) is the minimum number of guards sufficient to protect G from any length of any sequence of edge attacks. This paper derives the eternal vertex cover number τ^∞(G) of such graphs constructed by replacing each edge of a tree by an arbitrary elementary bipartite graph (or by an arbitrary clique), in terms of easily computable graph invariants only, thereby showing that τ^∞(G) can be computed in polynomial time for such graphs G.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E98.A (6), 1153-1160, 2015

  一般社団法人 電子情報通信学会

キーワード

• eternal vertex cover
• elementary bipartite graphs
• generalized trees

詳細情報

• CRID: 1390282681287535616
• NII論文ID: 130005071826
• DOI: 10.1587/transfun.e98.a.1153
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E98.A/6/E98.A_1153/_pdf
• 本文言語コード: en
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