Topology Atlas | Conferences

Knots in Washington XXXV
December 7-9, 2012
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

Conference Homepage


Genus ranges of 4-regular rigid vertex graphs
by
Masahico Saito
University of South Florida
Coauthors: Dorothy Buck, Egor Dolzhenko, Natasha Jonoska, Karin Valencia

The genus range of a graph is the set of values of genera over all surfaces into which the given graph is embedded cellularly, and we study the genus ranges of four-regular graphs with rigid vertices and a single transverse component. The genus ranges are shown to be sets of consecutive integers. Among consecutive integers satisfying the Euler characteristic formula, we investigate which sets can be, or cannot be, realized as genus ranges. Computer calculations are presented, and problems, conjectures are discussed.

Date received: November 2, 2012

Copyright © 2012 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbfw-18.