| Abstract: | Let  be k nonnegative integers. A graph G is  ‐colorable if the vertex set can be partitioned into k sets  , such that the subgraph  , induced by  , has maximum degree at most  for  . Let  denote the family of plane graphs with neither adjacent 3‐cycles nor 5‐cycles. Borodin and Raspaud (2003) conjectured that each graph in  is (0, 0, 0)‐colorable (which was disproved very recently). In this article, we prove that each graph in  is (1, 1, 0)‐colorable, which improves the results by Xu (2009) and Liu‐Li‐Yu (2016). |
