In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin（v） = {（s, t） ： E← a pair of maximum kite packings of order v intersecting in s blocks and s ＋ t...In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin（v） = {（s, t） ： E← a pair of maximum kite packings of order v intersecting in s blocks and s ＋ t triangles}. Let Adm（v） = {（s,t） ： s ＋ t≤by, s, t are non-negative integers}, where by = [v（v - 1）/8]. It is established that Fin（v） = Adm（v）／{（bv - 1,0）, （by - 1, 1）} for any integer v - 0, 1 （rood 8） and v ≥ 8; Fin（v） = Adm（v） for any integer v = 2, 3, 4, 5, 6, 7 （rood 8） and v≥ 4.展开更多
A decomposition of K_(n(g))∪Γ, the complete n-partite equipartite graph over gn vertices union a graph Γ(called the excess) that is a subgraph of K_(n(g)), into edge disjoint copies of a graph G is called a simple ...A decomposition of K_(n(g))∪Γ, the complete n-partite equipartite graph over gn vertices union a graph Γ(called the excess) that is a subgraph of K_(n(g)), into edge disjoint copies of a graph G is called a simple minimum group divisible covering of type g^n with G if Γ contains as few edges as possible. We examine all possible excesses for simple minimum group divisible(K_4-e)-coverings.Necessary and sufficient conditions are established for their existence.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities(Grant Nos.2011JBZ012 and 2011JBM298)National Natural Science Foundation of China(Grant Nos.61071221 and 10901016)
文摘In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin（v） = {（s, t） ： E← a pair of maximum kite packings of order v intersecting in s blocks and s ＋ t triangles}. Let Adm（v） = {（s,t） ： s ＋ t≤by, s, t are non-negative integers}, where by = [v（v - 1）/8]. It is established that Fin（v） = Adm（v）／{（bv - 1,0）, （by - 1, 1）} for any integer v - 0, 1 （rood 8） and v ≥ 8; Fin（v） = Adm（v） for any integer v = 2, 3, 4, 5, 6, 7 （rood 8） and v≥ 4.
基金Supported by NSFC(Grant Nos.11431003 and 11471032)Fundamental Research Funds for the Central Universities(Grant Nos.2016JBM071 and 2016JBZ012)
文摘A decomposition of K_(n(g))∪Γ, the complete n-partite equipartite graph over gn vertices union a graph Γ(called the excess) that is a subgraph of K_(n(g)), into edge disjoint copies of a graph G is called a simple minimum group divisible covering of type g^n with G if Γ contains as few edges as possible. We examine all possible excesses for simple minimum group divisible(K_4-e)-coverings.Necessary and sufficient conditions are established for their existence.
