2-factors and Independent Sets on Claw-free Graphs
نویسندگان
چکیده
In this paper, we show that if G is an l-connected claw-free graph with minimum degree at least three and l ∈ {2, 3}, then for any maximum independent set S, there exists a 2-factor in which each cycle contains at least l − 1 vertices in S.
منابع مشابه
Counting Independent Sets in Claw-Free Graphs
Although many of the counting problems (e.g. counting independent sets or matchings in a graph) are known to be #P-Complete (see Vadhan [3]), a remarkable progress has been done in designing exponential time algorithms solving them. Dahllöf, Jonsson, Wahlström [2] constructed algorithms that count maximum weight models of 2-SAT formulas in time O∗(1.2561n). This bound bound was later improved t...
متن کاملBounds on the Number of Vertex Independent Sets in a Graph
We consider the number of vertex independent sets i(G). In general, the problem of determining the value of i(G) is NP -complete. We present several upper and lower bounds for i(G) in terms of order, size or independence number. We obtain improved bounds for i(G) on restricted graph classes such as the bipartite graphs, unicyclic graphs, regular graphs and claw-free graphs.
متن کاملToughness and hamiltonicity in almost claw-free graphs
Some known results on claw-free (K 1;3-free) graphs are generalized to the larger class of almost claw-free graphs which were introduced by Ryjj a cek. In particular, we show that a 2-connected almost claw-free graph is 1-tough, and that a 2-connected almost claw-free graph on n vertices is hamiltonian if 1 3 (n ? 2), thereby (partly) generalizing results of Matthews and Sumner. Finally, we use...
متن کاملApproximating independence polynomials of claw-free graphs
Matchings in graphs correspond to independent sets in the corresponding line graphs. Line graphs are an important subclass of claw-free graphs. Hence studying independence polynomials of claw-free graphs is a natural extension of studying matching polynomials of graphs. We extend a result of Bayati et.al. showing a fully polynomial time approximation scheme (FPTAS) for computing the independenc...
متن کاملMaximum weight independent set for ℓclaw-free graphs in polynomial time
The MaximumWeight Independent Set (MWIS) problem is a well-known NPhard problem. A popular way to study MWIS is to detect graph classes for which MWIS can be solved in polynomial time, with particular reference to hereditary graph classes, i.e., defined by a hereditary graph property or equivalently by forbidding one or more induced subgraphs. For graphs G1, G2, G1 + G2 denotes the disjoint uni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 312 شماره
صفحات -
تاریخ انتشار 2012