【摘 要】
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We investigate the set of cycle lengths occurring in bipartite graphs with large minimum degree.A bipartite graph is weakly bipancyclic if it contains cycles of
【机 构】
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FacultyofMathematicsandStatistics,CentralChinaNormalUniversity
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We investigate the set of cycle lengths occurring in bipartite graphs with large minimum degree.A bipartite graph is weakly bipancyclic if it contains cycles of every even length between the length of a shortest and a longest cycle.In this talk, it is shown that if G =(V1, V2, E) is a bipartite graph with minimum degree at least n/3 + 4,where n =max {|V1|, |V2|}, then G is a weakly bipancyclic graph of girth 4.This improves a theorem of Tian and Zang [System Sci.Math Sci.2 (1989), 22-31], which asserts that if G is a Hamilton bipartite graph on 2n (n ≥ 60) vertices with minimum degree greater than 2n/5 + 2, then G is bipancyclic (i.e., G contains cycles of every even length between 4 and 2n).By combining our result with a theorem of Jackson and Li [J.Combin.Theory Ser.B 62 (1994), 236-258], we obtain that every 2-connected k-regular bipartite graph on at most 6k-38 vertices is bipancyclic.
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