Balanced 5-partitions Problems

If the vertex set of graph G is partitioned into k disjoint subsets,then the partition is said to be a k-partitions of graph G.A k-partitions of a graph is said to be balanced if ?Vi|-|Vj??1 for 1?i,j?k.In this dissertation,we mainly study balanced 5-partitions problems.The main results are as follows:1.Let G be a graph with n vertices and m edges such that ?(G)>4[n/5]and let r be a real number.Then G admits a maximum balanced 5-partitions V1,V2,V3,V4,V5 such that(?)if G satisfies:(1)(?)(2)(?)2.Let G be a graph with n vertices and m edges,and let p be the maximal number of pairwise vertex-disjoint K5 in Gc.Then G admits a minimum balanced 5-partitions V1,V2,V3,V4,V5 such that c(V1,V2,V3,V4,V5)?4/5m+2([n/5]-p)+6/5.