关键词: 均匀边染色, 均匀边色数阈值, 外1-平面图

Abstract: An [s]-equitable edge-[k]-coloringof a graph [G] is an edge coloring of [G] using [k] colors so that the sizes of any two color classes incident with any fixed vertex of [G] differ by at most [s]. The [s]-equitable edge chromatic threshold of [G] is the smallest [k] such that [G] has an [s]-equitable edge-[t]-colorings for integer [t] that is no less than [k]. It is proved that the 1-equitable edge chromatic threshold of any outer-1-planar graph is at most 5, the 1-equitable edge chromatic threshold of any outer-1-planar graph without adjacent triangles is at most 4, and the 2-equitable edge chromatic threshold of any outer-1-planar graph is exactly 1.

Key words: equitable edge coloring, equitable edge chromatic threshold, outer-1-planar graph