Independence Number of Graphs with a Prescribed Number of Cliques
نویسندگان
چکیده
منابع مشابه
Packing Cliques in Graphs with Independence Number 2
Let G be a graph with no three independent vertices. How many edges of G can be packed with edge-disjoint copies of Kk? More specifically, let fk(n,m) be the largest integer t such that for any graph with n vertices, m edges, and independence number 2, at least t edges can be packed with edge-disjoint copies ofKk. Turán’s Theorem together with Wilson’s Theorem assert that fk(n,m) = (1−o(1)) 2 4...
متن کاملOn the minimal number of k cliques in graphs with restricted independence number
We investigate the following problem of Erd1⁄2os: Determine the minimal number of k cliques in a graph of order n with independence number l: We disprove the original conjecture of Erd1⁄2os which was stated in 1962 for all but a nite number of pairs k; l; and give asymptotic estimates for l = 3; k 4 and l = 4; k 4: 1 Introduction Let tm (G) denote the number of complete subgraphs of order m in...
متن کاملMinimum Number of k-Cliques in Graphs with Bounded Independence Number
Let us give some definitions first. As usual, a graph G is a pair (V (G), E(G)), where V (G) is the vertex set and the edge set E(G) consists of unordered pairs of vertices. An isomorphism between graphs G and H is a bijection f : V (G) → V (H) that preserves edges and non-edges. For a graph G, let G = ( V (G), ( V (G) 2 ) \E(G) ) denote its complement and let v(G) = |V (G)| denote its order. F...
متن کاملNumber of Cliques in Graphs with a Forbidden Subdivision
We prove that for all positive integers t, every nvertex graph with no Kt-subdivision has at most 2 n cliques. We also prove that asymptotically, such graphs contain at most 2n cliques, where o(1) tends to zero as t tends to infinity. This strongly answers a question of D. Wood asking if the number of cliques in n-vertex graphs with no Kt-minor is at most 2 n for some constant c.
متن کاملon the number of cliques and cycles in graphs
we give a new recursive method to compute the number of cliques and cycles of a graph. this method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. in particular, let $g$ be a graph and let $overline {g}$ be its complement, then given the chromatic polynomial of...
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: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/7598