Let H=(V,E)be an n-balanced k-partite k-graph with partition classes V1,...,Vk.Suppose for every legal(k-1)-tuple f contained in V\V1 and for every legal(k-1)-tuple g contained in V\Vk such that f∪g■E(H),we have d(f...Let H=(V,E)be an n-balanced k-partite k-graph with partition classes V1,...,Vk.Suppose for every legal(k-1)-tuple f contained in V\V1 and for every legal(k-1)-tuple g contained in V\Vk such that f∪g■E(H),we have d(f)+d(g)≥n+1.In this paper,we prove that under this condition H must have a perfect matching.Another result of this paper is about the perfect matching in 3-uniform hm-bipartite hypergraphs.Let G be a 3-uniform hm-bipartite hypergraph with one of whose sides V1 has the size n,the another side V2 has size 2 n.If for all the legal 2-tuple f with|f∩V1|=1 and for all the legal 2-tuple g with|g∩V1|=0,we have d(f)≥n-2 and d(g)>n/2,then G has a perfect matching.展开更多
A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer ...A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer sequence π=(d 1,d 2,...,d n) is said to be graphic if it is the degree sequence of a simple graph G of order n and such a graph G is referred to as a realization of π . A graphic sequence π is said to be potentially P k graphic if it has a realization G having property P k . The problem: determine the smallest positive even number σ(k,n) such that every n term graphic sequence π=(d 1,d 2,...,d n) without zero terms and with degree sum σ(π)=d 1+d 2+...+d n at least σ(k,n) is potentially P k graphic has been proved positive.展开更多
基金supported in part by the National Natural Science Foundation of China (No. 61373019)
文摘Let H=(V,E)be an n-balanced k-partite k-graph with partition classes V1,...,Vk.Suppose for every legal(k-1)-tuple f contained in V\V1 and for every legal(k-1)-tuple g contained in V\Vk such that f∪g■E(H),we have d(f)+d(g)≥n+1.In this paper,we prove that under this condition H must have a perfect matching.Another result of this paper is about the perfect matching in 3-uniform hm-bipartite hypergraphs.Let G be a 3-uniform hm-bipartite hypergraph with one of whose sides V1 has the size n,the another side V2 has size 2 n.If for all the legal 2-tuple f with|f∩V1|=1 and for all the legal 2-tuple g with|g∩V1|=0,we have d(f)≥n-2 and d(g)>n/2,then G has a perfect matching.
文摘A variation in the classical Turn extremal problem is studied. A simple graph G of order n is said to have property P k if it contains a clique of size k+1 as its subgraph. An n term nonincreasing nonnegative integer sequence π=(d 1,d 2,...,d n) is said to be graphic if it is the degree sequence of a simple graph G of order n and such a graph G is referred to as a realization of π . A graphic sequence π is said to be potentially P k graphic if it has a realization G having property P k . The problem: determine the smallest positive even number σ(k,n) such that every n term graphic sequence π=(d 1,d 2,...,d n) without zero terms and with degree sum σ(π)=d 1+d 2+...+d n at least σ(k,n) is potentially P k graphic has been proved positive.
