Results 11 to 20 of about 1,999,234 (282)
Minimum Number of k-Cliques in Graphs with Bounded Independence Number [PDF]
, 2013 Erdos asked in 1962 about the value of f(n,k,l), the minimum number of k-cliques in a graph of order n and independence number less than l. The case (k,l)=(3,3) was solved by Lorden. Here we solve the problem (for all large n) when (k,l) is (3,4), (3,5),
Pikhurko, Oleg, Vaughan, Emil R.
core +2 more sources
Independence Number and Disjoint Theta Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a $\theta$-graph to be a pair of vertices $u, v$ with three internally disjoint paths joining $u$ to $v$. Given an independence number $\alpha$ and a fixed integer $k$, the results contained in this paper provide sharp bounds on the order $f(k, \alpha ...
Fujita, Shinya, Magnant, Colton
openaire +2 more sources
Independence densities of hypergraphs [PDF]
, 2013 We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs. Hypergraph independence densities include a broad family of densities over graphs and relational structures, such as ...
Bonato, Anthony +3 more
core +3 more sources
Shor’s bounds for the weighted independence number
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2019 Application of a technique of dual Lagrangian quadratic bounds of N.Z. Shor to studying the Maximum Weighted Independent Set problem is described. By the technique, two such N.Z. Shor’s upper bounds are obtained.
П. І. Стецюк +1 more
doaj +1 more source
On the k-Component Independence Number of a Tree
Discrete Dynamics in Nature and Society, 2021 Let G be a graph and k≥1 be an integer. A subset S of vertices in a graph G is called a k-component independent set of G if each component of GS has order at most k.
Shuting Cheng, Baoyindureng Wu
doaj +1 more source
On the Independence Number of Cayley Digraphs of Clifford Semigroups
Mathematics, 2023 Let S be a Clifford semigroup and A a subset of S. We write Cay(S,A) for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly path ...
Krittawit Limkul, Sayan Panma
doaj +1 more source
Source-Independent Quantum Random Number Generation [PDF]
Physical Review X, 2016 Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts---a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to ...
Zhu Cao +3 more
openaire +3 more sources
Further Results on Packing Related Parameters in Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets
Mojdeh Doost Ali +2 more
doaj +1 more source
Semi Square Stable Graphs and Efficient Dominating Sets [PDF]
Transactions on Combinatorics, 2023 A graph $G$ is called semi square stable if $\alpha (G^{2})=i(G)$ where $%\alpha (G^{2})$ is the independence number of $G^{2}$ and $i(G)$ is the independent dominating number of $G$.
Baha̓ Abughazaleh, Omar Abughneim
doaj +1 more source
The Independence Number of the Orthogonality Graph in Dimension $2^k$ [PDF]
, 2019 We determine the independence number of the orthogonality graph on $2^k$-dimensional hypercubes. This answers a question by Galliard from 2001 which is motivated by a problem in quantum information theory.
Ihringer, Ferdinand, Tanaka, Hajime
core +4 more sources