Balanced independent sets in graphs omitting large cliques
نویسندگان
چکیده
منابع مشابه
On the densities of cliques and independent sets in graphs
Let r, s ≥ 2 be integers. Suppose that the number of blue r-cliques in a red/blue coloring of the edges of the complete graph Kn is known and fixed. What is the largest possible number of red s-cliques under this assumption? The well known Kruskal-Katona theorem answers this question for r = 2 or s = 2. Using the shifting technique from extremal set theory together with some analytical argument...
متن کاملA Note on Independent Sets in Graphs with Large Minimum Degree and Small Cliques
Graphs with large minimum degree containing no copy of a clique on r vertices (Kr) must contain relatively large independent sets. A classical result of Andrásfai, Erdős, and Sós implies that Kr-free graphs G with degree larger than ((3r−7)/(3r− 4))|V (G)| must be (r− 1)-partite. An obvious consequence of this result is that the same degree threshold implies an independent set of order (1/(r − ...
متن کاملLarge Cliques and Stable Sets in Undirected Graphs
The cochromatic number of a graph G is the minimum number of stable sets and cliques of G covering the vertex-set of G. In this paper we survey some resent results and techniques developed in an attempt to answer the question: excluding which induced subgraphs causes a graph to have bounded cochromatic number?
متن کاملPartitioning chordal graphs into independent sets and cliques
We consider the following generalization of split graphs: A graph is said to be a (k, l)-graph if its vertex set can be partitioned into k independent sets and l cliques. (Split graphs are obtained by setting k = l = 1). Much of the appeal of split graphs is due to the fact that they are chordal, a property not shared by (k, l)-graphs in general. (For instance, being a (k, 0)-graph is equivalen...
متن کاملNeighborhood conditions for balanced independent sets in bipartite graphs
Let G be a balanced bipartite graph of order 2n and minimum degree (G) 3. If for every balanced independent set S of four vertices in G the neighborhood union jN(S)j > n then G is traceable, the circumference is at least 2n ? 2 and G contains a 2-factor (with one exceptional graph for the latter statement). If jN(S)j > n + 2 then G is hamiltonian.
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: Journal of Combinatorial Theory, Series B
سال: 2019
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2018.11.006