Results 11 to 20 of about 24,599 (177)
Large subgraphs without complete bipartite graphs [PDF]
, 2014 In this note, we answer the following question of Foucaud, Krivelevich and Perarnau. What is the size of the largest $K_{r,s}$-free subgraph one can guarantee in every graph $G$ with $m$ edges? We also discuss the analogous problem for hypergraphs.
Conlon, David +2 more
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Nonvanishing of Betti Numbers of Edge Ideals and Complete Bipartite Subgraphs [PDF]
Communications in Algebra, 2015 Given a finite simple graph one can associate the edge ideal. In this paper we prove that a graded Betti number of the edge ideal does not vanish if the original graph contains a set of complete bipartite subgraphs with some conditions. Also we give a combinatorial description for the projective dimension of the edge ideals of unmixed bipartite graphs.
Kimura, Kyouko
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AKCE International Journal of Graphs and Combinatorics, 2023 We introduce a concept in graph coloring motivated by the popular Sudoku puzzle. Let [Formula: see text] be a graph of order n with chromatic number [Formula: see text] and let [Formula: see text] Let [Formula: see text] be a k-coloring of the induced ...
J. Maria Jeyaseeli +3 more
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Covering Graphs with Few Complete Bipartite Subgraphs
Theoretical Computer Science, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fleischner, H. +3 more
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Total 2-Rainbow Domination Numbers of Trees
Discussiones Mathematicae Graph Theory, 2021 A 2-rainbow dominating function (2RDF) of a graph G = (V (G), E(G)) is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2} such that for every vertex v ∈ V (G) with f(v) = ∅ the condition ∪u∈N(v)f(u) = {1, 2} is fulfilled ...
Ahangar H. Abdollahzadeh +4 more
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On edge-sets of bicliques in graphs [PDF]
, 2012 A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-
Groshaus, Marina +2 more
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Uniform coverings of 2-paths with 4-cycles
AKCE International Journal of Graphs and Combinatorics, 2015 Let G be a graph [a digraph] and H be a subgraph of G. A D(G,H,λ) design is a multiset D of subgraphs of G each isomorphic to H so that every 2-path [directed 2-path] of G lies in exactly λ subgraphs in D.
Midori Kobayashi +3 more
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Algorithmic Aspects of Some Variants of Domination in Graphs
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 A set S ⊆ V is a dominating set in G if for every u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E, i.e., N[S] = V . A dominating set S is an isolate dominating set (IDS) if the induced subgraph G[S] has at least one isolated vertex.
Kumar J. Pavan, Reddy P.Venkata Subba
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On covering graphs by complete bipartite subgraphs
Discrete Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jukna, S., Kulikov, A.S.
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The Largest Complete Bipartite Subgraph in Point-Hyperplane Incidence Graphs [PDF]
The Electronic Journal of Combinatorics, 2020 Given $m$ points and $n$ hyperplanes in $\mathbb{R}^d$ ($d\geqslant 3)$, if there are many incidences, we expect to find a big cluster $K_{r,s}$ in their incidence graph. Apfelbaum and Sharir found lower and upper bounds for the largest size of $rs$, which match (up to a constant) only in three dimensions.
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