不含4-圈和7-圈环面图(F,F3)-分解的存在性

The Existence of(F,F3)-partition for Toroidal Graphs Without 4-and 7-cycles

令G=(V,E)是一个图.图G的(F,F_(d))-分解是指将G的顶点集合V(G)分解为2个子集V_(1)和V_(2),使得子图G[V_(1)]是森林,G[V_(2)]是最大度至多为d的森林.本文证明了每个不含4-圈和7-圈的环面图有(F,F_(3))-分解.

Let G=(V,E)be a graph.An(F,F_(d))-partition of a graph G is to divide the vertex set V(G)into two sets V_(1) and V_(2) such that G[V_(1)] is a forest and G[V_(2)] is the forest with bounded maximum degree at most d.In this paper,we prove that every toroidal graph without 4-cycles and 7-cycles admits an(F,F_(3))-partition.