Kotzig有向图的度偶序列

1.引言 设T_n是n阶竞赛图,V={v_1,v_2,…,v_n}是T_n的顶点集合。设扩v∈V,T_n中所有被v占优的顶点个数s(v)是v在T_n中的得分,记s(v_i)=s_i,i=1,2,…,n.将v_1,v_2,…,v_n重新排列,使s_1≤s_2≤…≤s_n,则S=(s_1,s_2,…,s_n)即是T_n的得分向量。 在Bondy与Murty的名著《图论及其应用》一书的末尾处列举了50个图论中未解决的问题,其中第45问题是:刻划所有n-1阶子竞赛图都同构的n阶竞赛图。这个问题是Kotzig 1973年提出的(见[1])。作者、黄国勋与林毓材研究了这个问题。文献     

t-可约竞赛图的得分向量

The definitions of t reducible and exactly t-reducible n tourna ments are introduced. Criteria are found for determining (i) whether a tourna ment with a given score vector R is t-reducible and (ii) whether it is exactly t-reducible.     

The smallest degree sum that yields potentially Kr,r-graphic sequences

We consider a variation of a classical Turán-type extremal problem as follows: Determine the smallest even integer σ(Kr,r, n) such that every n-term graphic sequence π = (d1, d2,..., dn) with term sum σ(π) = d1 + d2 +…+ dn ≥σ(Kr,r, n) is potentially Kr,r-graphic, where Kr,r is an r × r complete bipartite graph, i.e. πr has a realization G containing Kr,r as its subgraph. In this paper, the values σ(Kr,r,n) for even r and n ≥ 4r2 - r - 6 and for odd r and n ≥ 4r2 + 3r - 8 are determined.