In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
Let G(V,E) be a simple graph, the edge-binding number b1 (G) of G is defined as where N(S) denotes the adjacent edges set of S. In this paper, we obtained the edge-binding number of outer plane graphs, Halin graph and...Let G(V,E) be a simple graph, the edge-binding number b1 (G) of G is defined as where N(S) denotes the adjacent edges set of S. In this paper, we obtained the edge-binding number of outer plane graphs, Halin graph and tree.展开更多
A path factor of G is a spanning subgraph of G such that its each component is a path.A path factor is called a P≥n-factor if its each component admits at least n vertices.A graph G is called P≥n-factor covered if G...A path factor of G is a spanning subgraph of G such that its each component is a path.A path factor is called a P≥n-factor if its each component admits at least n vertices.A graph G is called P≥n-factor covered if G admits a P≥n-factor containing e for any e∈E(G),which is defined by[Discrete Mathematics,309,2067-2076(2009)].We first define the concept of a(P≥n,k)-factor-critical covered graph,namely,a graph G is called(P≥n,k)-factor-critical covered if G-D is P≥n-factor covered for any D⊆V(G)with|D|=k.In this paper,we verify that(i)a graph G withκ(G)≥k+1 is(P≥2,k)-factor-critical covered if bind(G)>2+k/3;(ii)a graph G with|V(G)|≥k+3 andκ(G)≥k+1 is(P≥3,k)-factor-critical covered if bind(G)≥4+k/3.展开更多
Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that...Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.展开更多
In this remark,we first simply survey the important results on component factors in graphs.Then,we focus on the binding number condition of component factors in some special settings.The main contributions in this rem...In this remark,we first simply survey the important results on component factors in graphs.Then,we focus on the binding number condition of component factors in some special settings.The main contributions in this remark are two folded:(1)we reveal that the existence of some special component factors is equal to some specific binding number conditions;(2)the parameter conditions for a graph G with a P≥3-factor are determined.展开更多
We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on...We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening(closure) of an energy bandgap at the center(boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.展开更多
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
基金the National Natural Science Foundation of China (No.19871036).
文摘Let G(V,E) be a simple graph, the edge-binding number b1 (G) of G is defined as where N(S) denotes the adjacent edges set of S. In this paper, we obtained the edge-binding number of outer plane graphs, Halin graph and tree.
基金Supported by Six Big Talent Peak of Jiangsu Province(Grant No.JY–022)333 Project of Jiangsu Provincethe National Natural Science Foundation of China(Grant No.11371009)。
文摘A path factor of G is a spanning subgraph of G such that its each component is a path.A path factor is called a P≥n-factor if its each component admits at least n vertices.A graph G is called P≥n-factor covered if G admits a P≥n-factor containing e for any e∈E(G),which is defined by[Discrete Mathematics,309,2067-2076(2009)].We first define the concept of a(P≥n,k)-factor-critical covered graph,namely,a graph G is called(P≥n,k)-factor-critical covered if G-D is P≥n-factor covered for any D⊆V(G)with|D|=k.In this paper,we verify that(i)a graph G withκ(G)≥k+1 is(P≥2,k)-factor-critical covered if bind(G)>2+k/3;(ii)a graph G with|V(G)|≥k+3 andκ(G)≥k+1 is(P≥3,k)-factor-critical covered if bind(G)≥4+k/3.
基金Supported by National Natural Science Foundation of China.
文摘Let integer k≥1, G be a graph of order n,n≥max {4k - 6, 4} and kn=0 (mod 2). Assume that the binding number of G is more than 2-2/n or the minimum degree of G is more than n/2. We prove that (i) G hasa k-fartor that contains a given edge; (ii) G has a k-factor that does not contain a given edge.
基金the National Natural Science Foundation of China(No.11761083).
文摘In this remark,we first simply survey the important results on component factors in graphs.Then,we focus on the binding number condition of component factors in some special settings.The main contributions in this remark are two folded:(1)we reveal that the existence of some special component factors is equal to some specific binding number conditions;(2)the parameter conditions for a graph G with a P≥3-factor are determined.
基金Project supported by the National Natural Science Foundation of China(Grant No.11405100)the Natural Science Basic Research Program in Shaanxi Province of China(Grant Nos.2022JZ-02,2020JM-507,and 2019JM-332)+1 种基金the Doctoral Research Fund of Shaanxi University of Science and Technology in China(Grant Nos.2018BJ-02 and 2019BJ-58)the Youth Innovation Team of Shaanxi Universities.
文摘We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening(closure) of an energy bandgap at the center(boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.
