## Abstract

Let G = (V, E) be a graph. A set I ⊆ V is independent if no two vertices from I are adjacent, and by Ind(G) we mean the family of all independent sets of G, while core(G) is the intersection of all maximum independent sets [4]. The number d_{c}(G) = max{{pipe}I{pipe} - {pipe}N(I){pipe}: I ∈ Ind(G)} is called the critical difference of G. A set X is critical if {pipe}X{pipe} - {pipe}N(X){pipe} = d_{c}(G) [10]. For a bipartite graph G = (A, B, E), Ore [7] defined δ_{0}(A) = max{{pipe}X{pipe} - {pipe}N(X){pipe}: X ⊆ A}. In this paper, we prove that d_{c}(G) = δ_{0}(A)+δ_{0}(B) and ker(G) = core(G) hold for every bipartite graph G = (A, B, E), where ker(G) denotes the intersection of all critical independent sets.

Original language | English |
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Pages (from-to) | 543-548 |

Number of pages | 6 |

Journal | Annals of Combinatorics |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2013 |

Externally published | Yes |

## Keywords

- critical set
- independent set
- matching