Partitioning 2‐Edge‐Colored Ore‐Type Graphs by Monochromatic Cycles

Abstract

Abstract Consider a graph G on n vertices satisfying the following Ore‐type condition: for any two nonadjacent vertices x and y of G , we have . We conjecture that if we color the edges of G with two colors then the vertex set of G can be partitioned to two vertex disjoint monochromatic cycles of distinct colors. In this article, we prove an asymptotic version of this conjecture.