A note on the girth-doubling construction for polygonal graphs

✍ Scribed by Ákos Seress; Eric Swartz

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 111 KB
• Volume: 68
• Category: Article
• ISSN: 0364-9024
• DOI: 10.1002/jgt.20555

✦ Synopsis

A near-polygonal graph is a graph which has a set C of m-cycles for some positive integer m such that each 2-path of is contained in exactly one cycle in C. If m is the girth of then the graph is called polygonal. Given a polygonal graph of valency r and girth m, Archdeacon and Perkel proved the existence of a polygonal graph 2 of valency r and girth 2m. We will show that this construction can be extended to one that yields a polygonal graph 3 of valency r and girth 3m, but that making the cycles any longer with this construction does not