Volume no :9, Issue no: 1, September (2018)

International Journal of Applied Mathematics and Machine Learning

THE LIGHT EDGES IN TOROIDAL GRAPHS WITHOUT ADJACENT 3- AND 4-CYCLES

Author's: Haihui Zhang
Pages: [1] - [5]
Received Date: July 2, 2018
Submitted by: Haiying Wang.
DOI: http://dx.doi.org/10.18642/ijamml_7100121987

Abstract

A subgraph of a graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. In this paper, we show that every toroidal graph with minimum vertex degree 3 and without adjacent 3- and 4-cycles has a light edge with the weight not greater than 9.

Keywords

toroidal graph, light edges, adjacent triangles.