Edge degree conditions for subpancyclicity in line graphs

✍ Scribed by Liming Xiong

• Book ID: 104114011
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 331 KB
• Volume: 188
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(97)00257-4

✦ Synopsis

In this paper, two best possible edge degree conditions are given for the line graph L(G) of a graph G with girth at least 4 or 5 to be subpaneyclic, i.e., L(G) contains a cycle of length k, for each k between 3 and the circumference of L(G). In [5] the following conjecture is made:

If G is a graph such that the degree sum of any pair of adjacent vertices in G is greater than

unless G is isomorphic to C4, C5, or the Petersen graph. Our results show that the conjecture is true for those graphs of order n>~72 with girth at least 4. (~