Tandem-win graphs

Clarke, Nancy E.; Nowakowski, Richard J.

doi:10.1016/j.disc.2004.11.016

Cited by 16 publications

(12 citation statements)

References 7 publications

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“…Combinatorial bounds (lower and upper) on the cop number results on different graph classes are discussed in [9,10,19,30,46,69,70,[91][92][93]110,117,118,145,161] Goldstein and Reingold [72] discussed the game on directed graphs. Different variations of the game with partial information can be found in [34,35,[37][38][39]43]. …”

Section: Search Variantsmentioning

confidence: 99%

An annotated bibliography on guaranteed graph searching

Fomin

Thilikos

2008

Theoretical Computer Science

279

165

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Section: Search Variantsmentioning

confidence: 99%

An annotated bibliography on guaranteed graph searching

Fomin

Thilikos

2008

Theoretical Computer Science

279

165

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“…Below we give a characterization of trianglefree k-winnable graphs, when there exists a search-free winning strategy for the cop. Compare Theorems 9 and 10 here with Theorems 8 and 9 in [5].…”

Section: Triangle-free K-winnable Graphsmentioning

confidence: 92%

“…The decomposition tree corresponding to one sequence of 2-corner retractions is shown in bold. This concept of decomposition tree is analogous to that of copwin spanning tree introduced in [8] and tandem-win decomposition tree introduced in [5]. Note that here, unlike with copwin and tandem-win trees (which involve one-point retractions), we are considering retractions in which multiple vertices are not fixed.…”

Section: Theorem 6 Let G Be a Graph Which Can Be Reduced To A Singlementioning

confidence: 94%

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A witness version of the Cops and Robber game

Clarke

2009

Discrete Mathematics

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a b s t r a c tThe games considered are mixtures of Searching and Cops and Robber. The cops have partial information provided via witnesses who report ''sightings'' of the robber. The witnesses are able to provide information about the robber's position but not the direction in which he is moving. The robber has perfect information. In the case when sightings occur at regular intervals, we present a recognition theorem for graphs on which a single cop suffices to guarantee a win. In a special case, this recognition theorem provides a characterization.

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“…In particular, known refinements of distance-preserving elimination orderings comprise the perfect elimination orderings [28], maximum neighbourhood orderings [6], h-extremal orderings [7], semisimplicial elimination orderings [24], dismantlable orderings [25] and more generally domination elimination orderings [19]. The latter orderings characterize chordal graphs, dually chordal graphs, homogeneously orderable graphs, cop-win graphs and a subclass of tandem-win graphs [12] respectively, and as above stated they all can be computed in polynomial-time when they exist. However the complexity of deciding whether a distance-preserving elimination ordering exists in a given graph has been left open until this paper.…”

Section: Introductionmentioning

confidence: 99%

On distance-preserving elimination orderings in graphs: Complexity and algorithms

Coudert

Ducoffe

Nisse

et al. 2018

Discrete Applied Mathematics

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For every connected graph G, a subgraph H of G is isometric if the distance between any two vertices in H is the same in H as in G. A distance-preserving elimination ordering of G is a total ordering of its vertex-set. . , v i ) with 1 ≤ i < n is isometric. This kind of ordering has been introduced by Chepoi in his study on weakly modular graphs [11]. We prove that it is NP-complete to decide whether such ordering exists for a given graph -even if it has diameter at most 2. Then, we prove on the positive side that the problem of computing a distance-preserving ordering when there exists one is fixed-parameter-tractable in the treewidth. Lastly, we describe a heuristic in order to compute a distance-preserving ordering when there exists one that we compare to an exact exponential time algorithm and to an ILP formulation for the problem.

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Tandem-win graphs

Cited by 16 publications

References 7 publications

An annotated bibliography on guaranteed graph searching

An annotated bibliography on guaranteed graph searching

A witness version of the Cops and Robber game

On distance-preserving elimination orderings in graphs: Complexity and algorithms

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