A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken ove...A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.展开更多
M. Matthews and D. Sumner proved that if G is a 2-connected claw-free graph of order n, then c(G) min{2δb + 4, n}. In this paper, we prove that if G is a,2-connected claw-free graph on n venices, then c(G) min{3δ + ...M. Matthews and D. Sumner proved that if G is a 2-connected claw-free graph of order n, then c(G) min{2δb + 4, n}. In this paper, we prove that if G is a,2-connected claw-free graph on n venices, then c(G) min{3δ + 2, n} or G belongs to one exceptional class of graphs.展开更多
It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory.Let V_(8)be a graph constructed from an 8-cycle by connecting the antipodal vertices.There are thirteen 2-connecte...It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory.Let V_(8)be a graph constructed from an 8-cycle by connecting the antipodal vertices.There are thirteen 2-connected spanning subgraphs of V_(8).In particular,one of them is obtained from the Petersen graph by deleting two vertices and it is also a hard problem to characterize Petersen-minor-free graphs.In this paper,we characterize internally 4-connected graphs which contain a 2-connected spanning subgraph of V_(8)as a forbidden minor.展开更多
A connected graph G is said to be a factor-critical graph if G - v has a perfect matching for every vertex v of G. In this paper, the 2-connected factor-critical graph G which has exactly ｜E（G）｜＋ 1 maximum matchi...A connected graph G is said to be a factor-critical graph if G - v has a perfect matching for every vertex v of G. In this paper, the 2-connected factor-critical graph G which has exactly ｜E（G）｜＋ 1 maximum matchings is characterized.展开更多
文摘A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components.The k-connected domination number γck（G） of G is the minimum cardinality taken over all minimal k-connected dominating sets of G.In this paper,we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.
文摘M. Matthews and D. Sumner proved that if G is a 2-connected claw-free graph of order n, then c(G) min{2δb + 4, n}. In this paper, we prove that if G is a,2-connected claw-free graph on n venices, then c(G) min{3δ + 2, n} or G belongs to one exceptional class of graphs.
基金Research Project supported by the National Natural Science Foundation of China(No.11961051)Provincial Natural Science Foundation of Shanxi(20210302123097)Shanxi Scholarship Council of China。
文摘It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory.Let V_(8)be a graph constructed from an 8-cycle by connecting the antipodal vertices.There are thirteen 2-connected spanning subgraphs of V_(8).In particular,one of them is obtained from the Petersen graph by deleting two vertices and it is also a hard problem to characterize Petersen-minor-free graphs.In this paper,we characterize internally 4-connected graphs which contain a 2-connected spanning subgraph of V_(8)as a forbidden minor.
基金supported by the National Natural Science Foundation of China(No.11551003)the Scientific research fund of the Science and Technology Program of Guangzhou,China(No.201510010265)the Qinghai Province Natural Science Foundation(No.2015-ZJ-911)
文摘A connected graph G is said to be a factor-critical graph if G - v has a perfect matching for every vertex v of G. In this paper, the 2-connected factor-critical graph G which has exactly ｜E（G）｜＋ 1 maximum matchings is characterized.
