Hamiltonian threshold for strong products of graphs

Kráľ, Daniel; Stacho, Ladislav

doi:10.1002/jgt.20314

Cited by 4 publications

(1 citation statement)

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“…This graph operation has been extensively investigated in relation to a wide range of subjects, including: connectivity [13], pancyclicity [14,15], chromaticity [16], bandwidth [17], independency [18,19] and primitivity [20]. Section 2 is devoted to introduce the main definitions and notation used throughout the paper.…”

Section: Introductionmentioning

confidence: 99%

On the geodetic and the hull numbers in strong product graphs

Cáceres

Hernando

Mora

et al. 2010

Computers & Mathematics with Applications

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A set S of vertices of a connected graph G is convex, if for any pair of vertices u,vS, every shortest path joining u and v is contained in S. The convex hull CH(S) of a set of vertices S is defined as the smallest convex set in G containing S. The set S is geodetic, if every vertex of G lies on some shortest path joining two vertices in S, and it is said to be a hull set if its convex hull is V(G). The geodetic and the hull numbers of G are the minimum cardinality of a geodetic and a minimum hull set, respectively. In this work, we investigate the behavior of both geodetic and hull sets with respect to the strong product operation for graphs. We also establish some bounds for the geodetic number and the hull number and obtain the exact value of these parameters for a number of strong product graphs.Peer ReviewedPostprint (published version

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Section: Introductionmentioning

confidence: 99%

On the geodetic and the hull numbers in strong product graphs

Cáceres

Hernando

Mora

et al. 2010

Computers & Mathematics with Applications

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Connectivity of Strong Products of Graphs

Špacapan

2010

Graphs and Combinatorics

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Cyclic colorings of plane graphs with independent faces

Azarija

Erman

Kráľ

et al. 2012

European Journal of Combinatorics

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Let G be a plane graph with maximum face size ∆ * . If all faces of G with size four or more are vertex disjoint, then G has a cyclic coloring with ∆ * + 1 colors, i.e., a coloring such that all vertices incident with the same face receive distinct colors. * This research was supported by the Czech-Slovenian bilateral project MEB 090805 (on the Czech side) and BI-CZ/08-09-005 (on the Slovenian side).

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Hamiltonian threshold for strong products of graphs

Abstract: Abstract:We prove that the strong product of any at least (ln 2) + O( √ ) non-trivial connected graphs of maximum degree at most is pancyclic. The obtained result is asymptotically best possible since the strong product of (ln 2)D stars K 1,D is not even hamiltonian.

Cited by 4 publications

References 10 publications

On the geodetic and the hull numbers in strong product graphs

On the geodetic and the hull numbers in strong product graphs

Connectivity of Strong Products of Graphs

Cyclic colorings of plane graphs with independent faces

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