Proof of Toft's Conjecture: Every Graph Containing No Fully Odd K4 Is 3-Colorable

Authors:
Wenan Zang
Affiliations:
-
Venue:
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Year:
1998

Citing 2
Cited 0

Stability critical graphs and even subdivisions of K4

Journal of Combinatorial Theory Series B
The four-colour theorem

Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday

Quantified Score

Hi-index	0.00

Visualization

Abstract

The graph 3-coloring problem arises in connection with certain scheduling and partition problems. As is well known, this problem is NP-complete and therefore intractable in general unless NP = P. The present paper is devoted to the 3-coloring problem on a large class of graphs, namely, graphs containing no fully odd K4, where a fully odd K4 is a subdivision of K4 such that each of the six edges of the K4 is subdivided into a path of odd length. In 1974, Toft conjectured that every graph containing no fully odd K4 can be vertex-colored with three colors. The purpose of this paper is to prove Toft's conjecture.