A vertex coloring of a graph G is called r-acyclic if it is a proper vertex coloring such that every cycle D receives at least min{｜D｜, r} colors. The r-acyclic chromatic number of G is the least number of colors in...A vertex coloring of a graph G is called r-acyclic if it is a proper vertex coloring such that every cycle D receives at least min{｜D｜, r} colors. The r-acyclic chromatic number of G is the least number of colors in an r-acyclic coloring of G. We prove that for any number r ≥ 4, the r-acyclic chromatic number of any graph G with maximum degree △ ≥ 7 and with girth at least（r-1）△ is at most（4r-3）△.展开更多
基金supported by NSFC(Grant number 11571258)SDNSF(Grant number ZR2016AM01)
文摘A vertex coloring of a graph G is called r-acyclic if it is a proper vertex coloring such that every cycle D receives at least min{｜D｜, r} colors. The r-acyclic chromatic number of G is the least number of colors in an r-acyclic coloring of G. We prove that for any number r ≥ 4, the r-acyclic chromatic number of any graph G with maximum degree △ ≥ 7 and with girth at least（r-1）△ is at most（4r-3）△.
