#### Title

The Perfect Graph Conjecture For Toroidal Graphs

#### Document Type

Article

#### Publication Date

1984

#### Published In

North-Holland Mathematics Studies

#### Abstract

This chapter discusses the perfect graph conjecture for toroidal graphs. Graphs are assumed to be finite without loops or multiple edges. The ω (G) is defined as the size of the largest complete subgraph of G, while γ (G) is defined as the vertex coloring number of G. A graph G is perfect only if G has property P. Each maximal clique of G intersects all but one maximal independent set of G, and vice versa. If G is toroidal and has property P, then G is perfect. In a critical toroidal graph G, either ω (G) < 4 or G is regular of degree six and triangulates the torus.

#### Recommended Citation

Charles M. Grinstead.
(1984).
"The Perfect Graph Conjecture For Toroidal Graphs".
*North-Holland Mathematics Studies*.
Volume 88,
97-101.
DOI: 10.1016/S0304-0208(08)72925-6

https://works.swarthmore.edu/fac-math-stat/202