Abstract
. For each vertex v in a graph G, the maximum length of a cycle which passes through v is called the cycle number of v, denoted by c(v). A sequence a 1,a 2,…,a n of nonnegative integers is called a cycle sequence of a graph G if the vertices of G can be labeled as v 1,v 2,…,v n such that a i =c(v i ) for 1≤i≤n. We give some sufficient and necessary conditions for a sequence to be a cycle sequence. We can thereby derive a polynomial time procedure for recognizing cycle sequences.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: July 14, 1997 Final version received: June 15, 1998
Rights and permissions
About this article
Cite this article
Lih, KW., Tong, LD. & Yan, JH. On Cycle Sequences. Graphs Comb 17, 129–133 (2001). https://doi.org/10.1007/PL00007234
Issue Date:
DOI: https://doi.org/10.1007/PL00007234