The bondage number of graphs with crossing number less than four

Yong Chang Cao, Jia Huang, Jun Ming Xu

Research output: Contribution to journalArticle

Abstract

The bondage number b(G) of a graph G is the smallest number of edges whose removal results in a graph with domination number greater than the domination number of G. Kang and Yuan [Bondage number of planar graphs. Discrete Math. 222(2000), 191-198] proved 6(G) ≤ min{8, Δ + 2} for every connected planar graph G, where Δ is the maximum degree of G. Later Carlson and Develin [On the bondage number of planar and directed graphs. Discrete Math. 306 (8-9) (2006), 820-826] presented a method to give a short proof for this result. This paper applies this technique to generalize the result of Kang and Yuan to any connected graph with crossing number less than four.

Original languageEnglish (US)
Pages (from-to)493-502
Number of pages10
JournalArs Combinatoria
Volume112
StatePublished - Oct 2013

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Bondage number
Crossing number
Planar graph
Domination number
Connected graph
Graph in graph theory
Maximum Degree
Directed Graph
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Keywords

  • Bondage number
  • Crossing number
  • Domination number
  • Planar graphs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The bondage number of graphs with crossing number less than four. / Cao, Yong Chang; Huang, Jia; Xu, Jun Ming.

In: Ars Combinatoria, Vol. 112, 10.2013, p. 493-502.

Research output: Contribution to journalArticle

Cao, Yong Chang ; Huang, Jia ; Xu, Jun Ming. / The bondage number of graphs with crossing number less than four. In: Ars Combinatoria. 2013 ; Vol. 112. pp. 493-502.
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