List 2-distance coloring for planar graphs with short circle constraints

Abstract

The [Formula: see text]-[Formula: see text]-distance coloring of the graph [Formula: see text] refers to that it satisfies the mapping: [Formula: see text], such that the vertex [Formula: see text] and [Formula: see text], whose distance is at most [Formula: see text], receive different colors, namely [Formula: see text]. Denote [Formula: see text]distancecoloring}, which is a list 2-distance chromatic number of the graph [Formula: see text]. This paper proves that [Formula: see text] for the graph [Formula: see text] without 3-cycles and intersecting 4-cycles and [Formula: see text].