A cycle C of a graph G is a m-distance-dominating cycle if for all vertices of . Defining denotes the minimum value of the degree sum of any k independent vertices of G. In this paper, we prove that if G is a 3-connec...A cycle C of a graph G is a m-distance-dominating cycle if for all vertices of . Defining denotes the minimum value of the degree sum of any k independent vertices of G. In this paper, we prove that if G is a 3-connected graph on n vertices, and if , then every longest cycle is m-distance-dominating cycles.展开更多
Let G be a graph and S a subset of vertices of G. In the paper we give a local condition on cycles in G dominating all vertices of S with large sums. We also derive some consequences on local hamiltonian conditions.
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
Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination numbe...Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc（G） = min{∑e∈E f（e）｜ f is an SCDF of G}. This paper will characterize all maxima] planar graphs G with order n ≥ 6 and γ′sc（G） =n.展开更多
Let F be a graph consisting of a triangle with a pendant leaf dangling from each vertex.A graph is{K_(1,3),F}-free if it contains no induced subgraph isomorphic to K_(1,3)or F.We give a stronger structural characteris...Let F be a graph consisting of a triangle with a pendant leaf dangling from each vertex.A graph is{K_(1,3),F}-free if it contains no induced subgraph isomorphic to K_(1,3)or F.We give a stronger structural characterisation of{K_(1,3),F}-free graph with which we obtain a more general result than that in[1]as follows:Given any two venices in a 2-connected{K_(1,3),F}-free graph,if there exists a shortest path between them containing no 2-cutset of the graph,then the graph has a Hamilton path cormecting these two venices.展开更多
Based on observations made during recent decades, reconstructed precipitation for the period A.D. 1736-2000, dry-wet index data for A.D. 500-2000, and a 1000-yr control simulation using the Community Earth System Mode...Based on observations made during recent decades, reconstructed precipitation for the period A.D. 1736-2000, dry-wet index data for A.D. 500-2000, and a 1000-yr control simulation using the Community Earth System Model with fixed pre-industrial external forcing, the decadal variability of summer precipitation over eastem China is stud- ied. Power spectrum analysis shows that the dominant cycles for the decadal variation of summer precipitation are： 22-24 and quasi-70 yr over the North China Plain; 32-36, 44-48, and quasi-70 yr in the Jiang-Huai area; and 32-36 and 4448 yr in the Jiang-Nan area. Bandpass decomposition from observation, reconstruction, and simulation re- veals that the variability of summer precipitation over the North China Plain, Jiang-Huai area, and Jiang-Nan area, at scales of 20-35, 35-50, and 50-80 yr, is not consistent across the entire millennium. We also find that the warm （cold） phase of the Pacific Decadal Oscillation generally corresponds to dry （wet） conditions over the North China Plain, but wet （dry） conditions in the Jiang-Nan area, from A.D. 1800, when the PDO became strengthened. However, such a correspondence does not exist throughout the entire last millennium. Data-model comparison sug- gests that these decadal oscillations and their temporal evolution over eastem China, including the decadal shifts in the spatial pattem of the precipitation anomaly observed in the late 1970s, early 1990s, and early 2000s, might result from internal variability of the climate system.展开更多
文摘A cycle C of a graph G is a m-distance-dominating cycle if for all vertices of . Defining denotes the minimum value of the degree sum of any k independent vertices of G. In this paper, we prove that if G is a 3-connected graph on n vertices, and if , then every longest cycle is m-distance-dominating cycles.
文摘Let G be a graph and S a subset of vertices of G. In the paper we give a local condition on cycles in G dominating all vertices of S with large sums. We also derive some consequences on local hamiltonian conditions.
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.
基金Supported by Doctoral Scientific Research Fund of Harbin Normal University(Grant No.KGB201008)
文摘Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc（G） = min{∑e∈E f（e）｜ f is an SCDF of G}. This paper will characterize all maxima] planar graphs G with order n ≥ 6 and γ′sc（G） =n.
基金This research is supported by the National Natural Science Foundation of China.
文摘Let F be a graph consisting of a triangle with a pendant leaf dangling from each vertex.A graph is{K_(1,3),F}-free if it contains no induced subgraph isomorphic to K_(1,3)or F.We give a stronger structural characterisation of{K_(1,3),F}-free graph with which we obtain a more general result than that in[1]as follows:Given any two venices in a 2-connected{K_(1,3),F}-free graph,if there exists a shortest path between them containing no 2-cutset of the graph,then the graph has a Hamilton path cormecting these two venices.
基金Supported by the National Natural Science Foundation of China(41430528 and 41471171)Institute of Geographic Sciences and Natural Resources Research,Chinese Academy of Sciences(TSYJS04,2014RC101,and 2015RC101)
文摘Based on observations made during recent decades, reconstructed precipitation for the period A.D. 1736-2000, dry-wet index data for A.D. 500-2000, and a 1000-yr control simulation using the Community Earth System Model with fixed pre-industrial external forcing, the decadal variability of summer precipitation over eastem China is stud- ied. Power spectrum analysis shows that the dominant cycles for the decadal variation of summer precipitation are： 22-24 and quasi-70 yr over the North China Plain; 32-36, 44-48, and quasi-70 yr in the Jiang-Huai area; and 32-36 and 4448 yr in the Jiang-Nan area. Bandpass decomposition from observation, reconstruction, and simulation re- veals that the variability of summer precipitation over the North China Plain, Jiang-Huai area, and Jiang-Nan area, at scales of 20-35, 35-50, and 50-80 yr, is not consistent across the entire millennium. We also find that the warm （cold） phase of the Pacific Decadal Oscillation generally corresponds to dry （wet） conditions over the North China Plain, but wet （dry） conditions in the Jiang-Nan area, from A.D. 1800, when the PDO became strengthened. However, such a correspondence does not exist throughout the entire last millennium. Data-model comparison sug- gests that these decadal oscillations and their temporal evolution over eastem China, including the decadal shifts in the spatial pattem of the precipitation anomaly observed in the late 1970s, early 1990s, and early 2000s, might result from internal variability of the climate system.
