Neighborhood unions and cyclability of graphs

Authors:
Huiqing Liu;Mei Lu;Feng Tian
Affiliations:
Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 10080, China;Department of Mathematical Sciences, Tsinghua University, Beijing 10084, China;Institute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 10080, China
Venue:
Discrete Applied Mathematics
Year:
2004

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Abstract

A graph G is said to be cyclable if for each orientation G of G, there exists a set S of vertices such that reversing all the arcs of G with one end in S results in a hamiltonian digraph. Let G be a 3-connected graph of order n ≥ 36. In this paper, we show that if for any three independent vertices x1, x2 and x3, |N(x1) ∪ N(x2)| + |N(x2) ∪ N(x3)| + |N(x3) ∪ N(x1)| ≥ 2n+1, then G is cyclable.