AN EXTENSION OF DHH-ERD ¨ OS CONJECTURE ON CYCLE-PLUS-TRIANGLE GRAPHS

Abstract

Consider $n$ disjoint triangles and a cycle on the 3$n$ vertices of the $n$ triangles. In 1986, Du, Hsu, and Hwang conjectured that the union of the $n$ triangles and the cycle has independent number $n$. Soon later, Paul Erd\"os improved it to a stronger version that every cycle-plus-triangle graph is 3-colorable. This conjecture was proved by H. Fleischner and M. Stiebitz. In this note, we want to give an extension of the above conjecture with an application in switching networks.