2-edge-Hamiltonian-connectedness of 4-connected plane graphs
نویسندگان
چکیده
منابع مشابه
2-edge-Hamiltonian-connectedness of 4-connected plane graphs
A graph G is called 2-edge-Hamiltonian-connected if for any X ⊂ {x1x2 : x1, x2 ∈ V (G)} with 1 ≤ |X| ≤ 2, G ∪ X has a Hamiltonian cycle containing all edges in X, where G ∪ X is the graph obtained from G by adding all edges in X. In this paper, we show that every 4-connected plane graph is 2edge-Hamiltonian-connected. This result is best possible in many senses and an extension of several known...
متن کاملHamiltonian connectedness in 3-connected line graphs
We investigate graphs G such that the line graph L(G) is hamiltonian connected if and only if L(G) is 3-connected, and prove that if each 3-edge-cut contains an edge lying in a short cycle of G, then L(G) has the above mentioned property. Our result extends Kriesell’s recent result in [J. of Combinatorial Theory, Ser. B. 82 (2001), 306-315] that every 4-connected line graph of a claw free graph...
متن کاملSome 3-connected 4-edge-critical non-Hamiltonian graphs
Let (G) be the domination number of graph G, thus a graph G is k -edge-critical if (G) 1⁄4 k ; and for every nonadjacent pair of vertices u and v, (Gþ uv) 1⁄4 k 1. In Chapter 16 of the book ‘‘Domination in Graphs— Advanced Topics,’’ D. Sumner cites a conjecture of E. Wojcicka under the form ‘‘3-connected 4-critical graphs are Hamiltonian and perhaps, in general (i.e., for any k 4), (k 1)-connec...
متن کاملZ3-connectivity of 4-edge-connected 2-triangular graphs
A graph G is k-triangular if each edge of G is in at least k triangles. It is conjectured that every 4-edge-connected 1-triangular graph admits a nowhere-zero Z3-flow. However, it has been proved that not all such graphs are Z3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z3-connected. The result is best possible. This result provides evidence to support t...
متن کاملGenerating connected and 2-edge connected graphs
We focus on the algorithm underlying the main result of [6]. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms. In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequentl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.06.033