Edge critical cops and robber

We consider edge critical graphs when playing cops and robber. Specifically, we look at those graphs whose copnumbers change from one to two when any edge is added, deleted, subdivided or contracted. We characterize all such sets, showing that they are empty, trees, all 2-edge-connected graphs and e...

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Bibliographic Details
Published inDiscrete mathematics Vol. 310; no. 17; pp. 2299 - 2309
Main Authors Clarke, N.E., Fitzpatrick, S.L., Hill, A., Nowakowski, R.J.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier B.V 28.09.2010
Elsevier
Subjects
Algebra
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Cop
Critical
Exact sciences and technology
Game
Graph
Graphs
Information retrieval. Graph
Mathematical analysis
Mathematics
Pursuit
Sciences and techniques of general use
Theoretical computing
Trees
Critical
Game
Graph
Pursuit
Cop
Edge(graph)
Tree(graph)
Discrete mathematics
Connected graph
Critical graph
Combinatorics
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Summary:We consider edge critical graphs when playing cops and robber. Specifically, we look at those graphs whose copnumbers change from one to two when any edge is added, deleted, subdivided or contracted. We characterize all such sets, showing that they are empty, trees, all 2-edge-connected graphs and empty, respectively. We also consider those graphs which change from copnumber two to one when any edge is added, and give a characterization in the k-regular case.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2010.05.004