Results for "Removable edges in a cycle of a 4-connected graph" in All Fields of Study

## Publications (6436)

• ### Removable edges in a cycle of a 4-connected graph(Citations: 1)

...if g " e is still 4-connected, then e is called a removable edge of g. in this paper, we investigate the problem on how many removable edges there are in a cycle of a 4-connected graph, and give examples to show...
Journal: Discrete Mathematics - DM , vol. 287, no. 1-3, pp. 103-111, 2004
• ### Removable Edges in 4Connected Graphs

...research on structural characterizations of graphs is a very popular topic in graph theory. the concepts of contractible edges and removable edges of graphs are powerful tools to study...we gave the following definition of removable edges in 4-connected graphs. definition: let \$g\$ be a 4-connected graph. for an edge \$e\$ of \$g\$, we perform the following...
• ### Removable edges in cycles of a k -connected graph(Citations: 1)

...n g−e (x). the existence of removable edges of k-connected graphs and some properties of 3-connected graphs and 4-connected graphs have been investigated. in the...graphs and study the distribution of removable edges on a cycle in a k-connected graph (k ≥ 4)....
Journal: Acta Mathematica Sinica-english Series - ACTA MATH SIN-ENGLISH SERIES , vol. 27, no. 4, pp. 781-788, 2011
• ### Removable edges of cycles in 5-connected graphs

...from g−e and then completely connect the 4 neighbors of x by k 4. if multiple edges occur, we use single edge to replace them. the final...paper, we investigate the distribution of removable edges in a cycle of a 5-connected graph. and we give examples to...
Journal: Journal of Applied Mathematics and Computing , vol. 28, no. 1, pp. 93-106, 2008
• ### Removable Edges in Longest Cycles of 4Connected Graphs(Citations: 1)

...e. if g⊖ e is 4-connected, then e is called a removable edge of g. in this paper we obtain some results on removable edges in a longest cycle of a 4-connected graph g. we also show that...
Journal: Graphs and Combinatorics , vol. 20, no. 3, pp. 413-422, 2004
• ### Non removable edges in 3-connected cubic graphs

...letg be a cyclicallyk-edge-connected cubic graph withk = 3. lete be an edge ofg. letg' be the cubic graph obtained fromg by deletinge and...edgee is said to bek-removable ifg' is also cyclicallyk-edge-connected. let us denote by sk(g)> the graph induced by thek-removable edges and by nk(g)>...
Journal: Graphs and Combinatorics , vol. 7, no. 2, pp. 119-141, 1991
• ### Complexes of not \$i\$-connected graphs(Citations: 57)

...complexes of (not) connected graphs, hypergraphs and their homology appear in the construction of knot invariants given by v. vassiliev. in this paper we study the...we show that the complex of not \$2\$-connected graphs has the homotopy type of a wedge of \$(n-2)!\$ spheres of dimension \$2n-5\$. this answers...
Journal: Topology , 1997
• ### Removable edges in a 5-connected graph and a construction method of 5-connected graphs(Citations: 4)

...nontrivial k-separator. the existence of removable edges of 3-connected and 4-connected graphs and some properties of quasi k-connected graphs have been investigated [d.a. holton, b. jackson, a. saito, n.c. wormale, removable edges in 3-connected graphs, j. graph theory 14(4) (1990) 465–473; h. jiang...
Journal: Discrete Mathematics - DM , vol. 308, no. 9, pp. 1726-1731, 2008
• ### Sparse certificates and removable cycles in l-mixed p-connected graphs(Citations: 3)

...l|p. this notion is a common generalisation of m-vertex-connectivity (l=1,p=m) and m-edge-connectivity (l⩾m, p=m). we show...to find sparse certificates and removable cycles in l-mixed p-connected graphs in linear time....
Journal: Operations Research Letters - ORL , vol. 33, no. 2, pp. 111-114, 2005
• ### On Small Contractible Subgraphs in 3-connected Graphs of Small Average Degree(Citations: 1)

...we study the distribution of small contractible subgraphs in 3-connec- ted graphs under local regularity conditions. ams...
Journal: Graphs and Combinatorics , vol. 23, no. 5, pp. 545-557, 2007