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Upper bounds for inverse domination in graphs
Theory and Applications of Graphs, 2021 In any graph $G$, the domination number $\gamma(G)$ is at most the independence number $\alpha(G)$. The \emph{Inverse Domination Conjecture} says that, in any isolate-free $G$, there exists pair of vertex-disjoint dominating sets $D, D'$ with $|D|=\gamma(
Elliot Krop +2 more
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Facial rainbow edge-coloring of simple 3-connected plane graphs [PDF]
Opuscula Mathematica, 2020 A facial rainbow edge-coloring of a plane graph \(G\) is an edge-coloring such that any two edges receive distinct colors if they lie on a common facial path of \(G\).
Július Czap
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Core Index of Perfect Matching Polytope for a 2-Connected Cubic Graph
Discussiones Mathematicae Graph Theory, 2018 For a 2-connected cubic graph G, the perfect matching polytope P(G) of G contains a special point xc=(13,13,…,13)$x^c = \left( {{1 \over 3},{1 \over 3}, \ldots ,{1 \over 3}} \right)$ . The core index ϕ(P(G)) of the polytope P(G) is the minimum number of
Wang Xiumei, Lin Yixun
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Virtual Betti numbers of mapping tori of 3-manifolds
, 2020 Given a reducible $3$-manifold $M$ with an aspherical summand in its prime decomposition and a homeomorphism $f\colon M\to M$, we construct a map of degree one from a finite cover of $M\rtimes_f S^1$ to a mapping torus of a certain aspherical $3 ...
Neofytidis, Christoforos
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The mod 2 Margolis homology of the Dickson algebra
Comptes Rendus. Mathématique, 2020 We completely compute the mod 2 Margolis homology of the Dickson algebra $D_n$, i.e. the homology of $D_n$ with the differential to be the Milnor operation $Q_j$, for every $n$ and $j$.
Hưng, Nguyễn H. V.
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A related problem on s-Hamiltonian line graphs
AIMS Mathematics, 2022 A graph $ G $ is said to be claw-free if $ G $ does not contain $ K_{1, 3} $ as an induced subgraph. For an integer $ s\geq0 $, $ G $ is $ s $-Hamiltonian if for any vertex subset $ S\subset V(G) $ with $ |S|\leq s $, $ G-S $ is Hamiltonian.
Xia Liu
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, 2017 Let f(1)=1, and let f(n+1)=2^{2^{f(n)}} for every positive integer n. We conjecture that if a system S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} \cup {x_i+1=x_k: i,k \in {1,...,n}} has only finitely many solutions in non-negative integers x_1,...
Tyszka, Apoloniusz
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Vertex-coloring edge-weightings: Towards the 1-2-3-conjecture
Journal of Combinatorial Theory, Series B, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kalkowski, Maciej +2 more
openaire +2 more sources
Weak and Strong Versions of the 1-2-3 Conjecture for Uniform Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2016 Given an $r$-uniform hypergraph $H=(V,E)$ and a weight function $\omega:E\to\{1,\dots,w\}$, a coloring of vertices of~$H$, induced by~$\omega$, is defined by $c(v) = \sum_{e\ni v} w(e)$ for all $v\in V$. If there exists such a coloring that is strong (that means in each edge no color appears more than once), then we say that $H$ is strongly $w ...
Bennett, Patrick +3 more
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Sickle Cell Disease Is an Inherent Risk for Asthma in a Sibling Comparison Study
Pediatric Blood &Cancer, EarlyView.ABSTRACT Introduction Sickle cell disease (SCD) and asthma share a complex relationship. Although estimates vary, asthma prevalence in children with SCD is believed to be comparable to or higher than the general population. Determining whether SCD confers an increased risk for asthma remains challenging due to overlapping symptoms and the ...
Suhei C. Zuleta De Bernardis +9 more
wiley +1 more source