5^——圈和5^——圈不交的平面图的injective-列表染色

Injective list coloring of planar graphs with disjoint 5^--cycles and 5^--cycles

通过构造一个(Δ+6)-临界图,运用权转移的方法证明了:对于5^--圈和5^--圈不交且Δ(G)≥18的平面图G,有χi^l(G)≤Δ(G)+6.所得结果研究了平面图G在短圈不交的限制条件下的injective-列表染色的问题.

It was studied a plane graph G with disjoint 5^--cycles and 5^--cycles,withχi(G)as its injective chromatice number.It was improved some known result by proving thatχi^l(G)≤Δ+6 whenΔ(G)≥18.The result was obtained by contradiction:if G was supposed to be a(Δ+6)-critical graph,a discharging procedure was then applied to the proof by showing that G could not exist.This conclusion would contribute to the studies the problem of injective-list coloring for plane G without disjoint cycles.