Coloring graphs without induced 5 or 5-5-e

We use P5 to denote a path of length 5 and C5 to denote a cycle of length 5. The aim of this paper is to prove that, if G is a connected graph satisfying (1). G has an induced C5 and no clique cut-set, (2). G has no induced subgraph isomorphic toPK5 or K5 - G, then G is max{13, (13) + 1}-colorable.

Automated summary

The aim of this paper is to prove that a connected graph satisfying certain conditions is colorable.