Forcing faces in plane bipartite graphs (II)

Zhongyuan Che, Zhibo Chen

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The concept of forcing faces of a plane bipartite graph was first introduced in Che and Chen (2008) [3] [Z. Che, Z. Chen, Forcing faces in plane bipartite graphs, Discrete Mathematics 308 (2008) 2427-2439], which is a natural generalization of the concept of forcing hexagons of a hexagonal system introduced in Che and Chen (2006) [2] [Z. Che and Z. Chen, Forcing hexagons in hexagonal systems, MATCH Commun. Math. Comput. Chem. 56 (2006) 649-668]. In this paper, we further extend this concept from finite faces to all faces (including the infinite face) as follows: A face s (finite or infinite) of a 2-connected plane bipartite graph G is called a forcing face if the subgraph G - V(s) obtained by removing all vertices of s together with their incident edges has exactly one perfect matching. For a plane elementary bipartite graph G with more than two vertices, we give three necessary and sufficient conditions for G to have all faces forcing. We also give a new necessary and sufficient condition for a finite face of G to be forcing in terms of bridges in the Z-transformation graph Z(G) of G. Moreover, for the graphs G whose faces are all forcing, we obtain a characterization of forcing edges in G by using the notion of handle, from which a simple counting formula for the number of forcing edges follows.

Original languageEnglish (US)
Pages (from-to)71-80
Number of pages10
JournalDiscrete Applied Mathematics
Volume161
Issue number1-2
DOIs
StatePublished - Jan 1 2013

Fingerprint

Plane Graph
Bipartite Graph
Forcing
Face
Hexagon
Necessary Conditions
Graph Transformation
Sufficient Conditions
Perfect Matching
Discrete mathematics
Subgraph
Counting

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Che, Zhongyuan ; Chen, Zhibo. / Forcing faces in plane bipartite graphs (II). In: Discrete Applied Mathematics. 2013 ; Vol. 161, No. 1-2. pp. 71-80.
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Forcing faces in plane bipartite graphs (II). / Che, Zhongyuan; Chen, Zhibo.

In: Discrete Applied Mathematics, Vol. 161, No. 1-2, 01.01.2013, p. 71-80.

Research output: Contribution to journalArticle

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