## Abstract

Given a class C of graphs, a graph G = (V, E) is said to be a C-probe graph if there exists a stable (i.e., independent) set of vertices X ⊆ V and a set F of pairs of vertices of X such that the graph G^{′} = (V, E ∪ F) is in the class C. Recently, there has been increasing interest and research on a variety of C-probe graph classes, such as interval probe graphs, chordal probe graphs and chain probe graphs. In this paper we focus on chordal-bipartite probe graphs. We prove a structural result that if B is a bipartite graph with no chordless cycle of length strictly greater than 6, then B is chordal-bipartite probe if and only if a certain "enhanced" graph B^{*} is a chordal-bipartite graph. This theorem is analogous to a result on interval probe graphs in Zhang (1994) [18] and to one on chordal probe graphs in Golumbic and Lipshteyn (2004) [11].

Original language | English |
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Pages (from-to) | 193-197 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 110 |

Issue number | 5 |

DOIs | |

State | Published - 1 Feb 2010 |

## Keywords

- Chordal bipartite graphs
- Combinatorial problems
- Probe graphs

## ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications