Plane Elementary Bipartite Graphs with Forcing or Anti-forcing Edges

Zhongyuan Che, Zhibo Chen

Research output: Contribution to journalArticle

Abstract

Let G be a plane elementary bipartite graph with more than one finite face. We first characterize forcing edges and anti-forcing edges of G in terms of handles and forcing faces. We then introduce the concept of a nice pair of faces of G, which allows us to provide efficient algorithms to construct plane minimal elementary bipartite graphs from G. We show that if G is a minimal elementary spanning subgraph of G, then all vertices of a forcing face of G are contained in a forcing face of G, and any forcing face of G is a forcing face of G if it is still a face of G. Furthermore, any forcing edge (resp., anti-forcing edge) of G is still a forcing edge (resp., an anti-forcing edge) of G if it is still an edge of G. We conclude the paper with the co-existence property of forcing edges and anti-forcing edges for those plane minimal elementary bipartite graphs that remain 2-connected when any handle of length one (if exists) is deleted.

Original languageEnglish (US)
Pages (from-to)959-971
Number of pages13
JournalGraphs and Combinatorics
Volume35
Issue number4
DOIs
StatePublished - Jul 1 2019

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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