For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain th...For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.展开更多
In 1989, Zhu, Li and Deng introduced the definition of implicit degree of a vertex v in a graph G, denoted by id（v）. In this paper, we prove that if G is a 2-connected graph of order n such that id（u） ＋ id（v） ...In 1989, Zhu, Li and Deng introduced the definition of implicit degree of a vertex v in a graph G, denoted by id（v）. In this paper, we prove that if G is a 2-connected graph of order n such that id（u） ＋ id（v） ≥ n for each pair of nonadjacent vertices u and v in G, then G is pancyclic unless G is bipartite, or else n = 4r, r ≥ 2 and G is isomorphic to F4r .展开更多
Content-Centric Networking is a novel future network architecture that attracts increasing research interests in recent years. In-network caching has been regarded as a prominent feature of Content-Centric Networking ...Content-Centric Networking is a novel future network architecture that attracts increasing research interests in recent years. In-network caching has been regarded as a prominent feature of Content-Centric Networking since it is able to reduce the network traffic, alleviate the server bottleneck and decrease the user access latency. However, the CCN default caching scheme results in a high caching redundancy, causing an urgent need for an efficient caching scheme. To address this issue, we propose a novel implicit cooperative caching scheme to efficiently reduce the caching redundancy and improve the cache resources utilization. The simulation results show that our design achieves a higher hit ratio and a shorter cache hit distance in comparison with the other typical caching schemes.展开更多
In 2005,Flandrin et al.proved that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that d(x)+d(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,··...In 2005,Flandrin et al.proved that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that d(x)+d(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,···,k,then G is hamiltonian.In order to get more sufficient conditions for hamiltonicity of graphs,Zhu,Li and Deng proposed the definitions of two kinds of implicit degree of a vertex v,denoted by id1(v)and id2(v),respectively.In this paper,we are going to prove that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that id2(x)+id2(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,···,k,then G is hamiltonian.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11501322)the Postdoctoral Science Foundation of China(Grant No.2015M571999)the Natural Science Foundation of Shandong Province(Grant No.ZR2014AP002)
文摘For a graph G, we denote by p（G） and c（G） the number of vertices of a longest path and a longest cycle in G, respectively. For a vertex v in G, id（v） denotes the implicit degree of v. In this paper, we obtain that if G is a 2-connected graph on n vertices such that the implicit degree sum of any three independent vertices is at least n ＋ 1, then either G contains a hamiltonian path, or c（G） 〉 p（G） - 1.
文摘In 1989, Zhu, Li and Deng introduced the definition of implicit degree of a vertex v in a graph G, denoted by id（v）. In this paper, we prove that if G is a 2-connected graph of order n such that id（u） ＋ id（v） ≥ n for each pair of nonadjacent vertices u and v in G, then G is pancyclic unless G is bipartite, or else n = 4r, r ≥ 2 and G is isomorphic to F4r .
基金supported in part by the 973 Program under Grant No.2013CB329100in part by NSFC under Grant No.61422101,62171200,and 62132017+1 种基金in part by the Ph.D. Programs Foundation of MOE of China under Grant No.20130009110014in part by the Fundamental Research Funds for the Central Universities under Grant No.2016JBZ002
文摘Content-Centric Networking is a novel future network architecture that attracts increasing research interests in recent years. In-network caching has been regarded as a prominent feature of Content-Centric Networking since it is able to reduce the network traffic, alleviate the server bottleneck and decrease the user access latency. However, the CCN default caching scheme results in a high caching redundancy, causing an urgent need for an efficient caching scheme. To address this issue, we propose a novel implicit cooperative caching scheme to efficiently reduce the caching redundancy and improve the cache resources utilization. The simulation results show that our design achieves a higher hit ratio and a shorter cache hit distance in comparison with the other typical caching schemes.
基金supported by the National Natural Science Foundation of China (No.11501322)Scientific Research Foundation for Doctors in Qufu Normal University (No. 2012015)Natural Science Foundation of Qufu Normal University (No.xkj201415)
文摘In 2005,Flandrin et al.proved that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that d(x)+d(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,···,k,then G is hamiltonian.In order to get more sufficient conditions for hamiltonicity of graphs,Zhu,Li and Deng proposed the definitions of two kinds of implicit degree of a vertex v,denoted by id1(v)and id2(v),respectively.In this paper,we are going to prove that if G is a k-connected graph of order n and V(G)=X1∪X2∪···∪Xk such that id2(x)+id2(y)≥n for each pair of nonadjacent vertices x,y∈Xi and each i with i=1,2,···,k,then G is hamiltonian.
