THE INDEPENDENCE NUMBER OF CONNECTED (claw, $K_4$)-FREE 4-REGULAR GRAPHS
نویسندگان
چکیده
منابع مشابه
4-regular claw-free IM-extendable graphs
A graph G is induced matching extendable (shortly, IM-extendable), if every induced matching of G is included in a perfect matching of G. A graph G is claw-free, if G does not contain any induced subgraph isomorphic toK1,3. The kth power of a graphG, denoted byGk , is the graph with vertex set V (G) in which two vertices are adjacent if and only if the distance between them in G is at most k. I...
متن کاملPancyclicity of 4-Connected, Claw-Free, P10-Free Graphs
A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V (G)|. We show that if G is 4-connected, claw-free, and P10-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pai...
متن کاملQuadrangularly connected claw-free graphs
A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of l-cycles (3 ≤ l ≤ 4) C1, C2, ..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) 6= ∅ for i = 1, 2, ..., r − 1. In this paper, we show that every quadrangularly connected claw-free graph without vertices of degree 1, which does not contain an induced subgraph H isomorphic to eithe...
متن کاملOn factors of 4-connected claw-free graphs
We consider the existence of several different kinds of factors in 4-connected claw-free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4-connected line graph is hamiltonian, i.e. has a connected 2-factor. Conjecture 2 (Matthews and Sumner): Every 4-connected claw-free graph is hamil...
متن کاملPancyclicity of 4-connected {claw, generalized bull}-free graphs
A graph G is pancyclic if it contains cycles of each length `, 3 ≤ ` ≤ |V (G)|. The generalized bull B(i, j) is obtained by associating one endpoint of each of the paths Pi+1 and Pj+1 with distinct vertices of a triangle. Gould, Luczak and Pfender [4] showed that if G is a 3-connected {K1,3, B(i, j)}-free graph with i + j = 4 then G is pancyclic. In this paper, we prove that every 4-connected, ...
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: Taiwanese Journal of Mathematics
سال: 2013
ISSN: 1027-5487
DOI: 10.11650/tjm.17.2013.2189