Results 11 to 20 of about 9,407,399 (300)
The critical independence number and an independence decomposition [PDF]
European Journal of Combinatorics, 2011 An independent set Ic is a critical independent set if |Ic|−|N(Ic)|≥|J|−|N(J)|, for any independent set J. The critical independence number of a graph is the cardinality of a maximum critical independent set.
Larson, C.E., C.E. Larson
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On the strength and independence number of graphs [PDF]
Contributions to Mathematics, 2022 Rikio Ichishima +2 more
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On the signed $2$-independence number of graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2017 In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach.
S.M. Hosseini Moghaddam +3 more
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On Selkow’s Bound on the Independence Number of Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G with vertex set V (G) and independence number α(G), Selkow [A Probabilistic lower bound on the independence number of graphs, Discrete Math. 132 (1994) 363–365] established the famous lower bound ∑v∈V(G)1d(v)+1(1+max{d(v)d(v)+1-∑u∈N(v)1d(u)+
Harant Jochen, Mohr Samuel
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On the number of independent orders [PDF]
Annals of Pure and Applied Logic, 2021 We investigate a model theoretic invariant $κ_{srd}^m(T)$, which was introduced by Shelah in his famous book, and prove that $κ_{srd}^m(T)$ is sub-additive. When $κ_{srd}^m(T)$ is infinite, this gives the equality $κ^m_{srd}(T)=κ^1_{srd}(T)$, answering a question by Shelah. We apply the same proof method to analyze another invariant $κ^m_{ird}(T)$, and
Kota Takeuchi, Akito Tsuboi
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On the Stability of the Graph Independence Number [PDF]
SIAM Journal on Discrete Mathematics, 2022 Let $G$ be a graph on $n$ vertices of independence number $α(G)$ such that every induced subgraph of $G$ on $n-k$ vertices has an independent set of size at least $α(G) - \ell$. What is the largest possible $α(G)$ in terms of $n$ for fixed $k$ and $\ell$? We show that $α(G) \le n/2 + C_{k, \ell}$, which is sharp for $k-\ell \le 2$.
Zichao Dong, Zhuo Wu
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On the broadcast independence number of caterpillars [PDF]
Discrete Applied Mathematics, 2018 Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f : V(G)\rightarrow\mathbb{N}$ such that $f(v)\le e\_G(v)$ holds for every vertex $v$ of $G$, where $e\_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum distance from $v$ to any other vertex of $G$.The cost of $f$ is the value ${\rm cost}(f)=\sum\_{v\in V(G)}f(v)$.A
Messaouda Ahmane +2 more
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Relating the independence number and the dissociation number
Journal of Graph Theory, 2023 AbstractThe independence number and the dissociation number of a graph are the largest orders of induced subgraphs of of maximum degree at most 0 and at most 1, respectively. We consider possible improvements of the obvious inequality . For connected cubic graphs distinct from , we show , and describe the rich and interesting structure of the ...
Felix Bock +3 more
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Independent [1,2]-number versus independent domination number [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2017 Abstract A [1; 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every graph. In this paper we provide local conditions, depending on the degree of
Aleid, Sahar A. +2 more
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A generalization of the independence number
Discrete Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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