Premium
Edge disjoint cycles in graphs
Author(s) -
Hao Li
Publication year - 1989
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190130306
Subject(s) - combinatorics , mathematics , disjoint sets , hamiltonian path , graph , pancyclic graph , hamiltonian (control theory) , discrete mathematics , line graph , 1 planar graph , mathematical optimization
Ore proved in 1960 that if G is a graph of order n and the sum of the degrees of any pair of nonadjacent vertices is at least n , then G has a hamiltonian cycle. In 1986, Li Hao and Zhu Yongjin showed that if n ⩾ 20 and the minimum degree δ is at least 5, then the graph G above contains at least two edge disjoint hamiltonian cycles. The result of this paper is that if n ⩾ 2δ 2 , then for any 3 ⩽ l 1 ⩽ l 2 ⩽ ⃛ ⩽ l k ⩽ n , 1 = k = [(δ ‐ 1)/2], such graph has K edge disjoint cycles with lengths l 1 , l 2 …l k , respectively. In particular, when l 1 = l 2 = ⃛ = l k = n and k = [(δ ‐ 1)/2], the graph contains [(δ ‐ 1)/2] edge disjoint hamiltonian cycles.