Results 21 to 30 of about 2,369,458 (297)
Ultrafilters and Independent Sets [PDF]
Transactions of the American Mathematical Society, 1972 Independent families of sets and of functions are used to prove some theorems about ultrafilters. All of our results are well known to be provable from some form of the generalized continuum hypothesis, but had remained open without such an assumption.
openaire +1 more source
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
doaj +1 more source
Independent Sets in Polarity Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2016 Given a projective plane $ $ and a polarity $ $ of $ $, the corresponding polarity graph is the graph whose vertices are the points of $ $, and two distinct points $p_1$ and $p_2$ are adjacent if $p_1$ is incident to $p_2^{ }$ in $ $. A well-known example of a polarity graph is the Erd s-R nyi orthogonal polarity graph $ER_q$, which appears ...
Tait, Michael, Timmons, Craig
openaire +3 more sources
Independent Sets In Association Schemes [PDF]
Combinatorica, 2006 15 pages; This is the corrected version that will appear in ...
Godsil, C. D., Newman, M. W.
openaire +2 more sources
Discrete Applied Mathematics, 2016 The regular independence number, introduced by Albertson and Boutin in 1990, is the size of a largest set of independent vertices with the same degree. Lower bounds were proven for this invariant, in terms of the order, for trees and planar graphs.
Yair Caro, Adriana Hansberg, Ryan Pepper
openaire +3 more sources
Independent sets in algebraic hypergraphs
Journal of the European Mathematical Society, 2021 In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, in the spirit of the so-called transference principles in extremal combinatorics, that if a given algebraic hypergraph is “dense” in a certain sense, then a generic low-dimensional subset of its vertices induces a subhypergraph that is also “dense.” (For
Anton Bernshteyn +2 more
openaire +2 more sources
On the number of maximum independent sets of graphs [PDF]
Transactions on Combinatorics, 2014 Let $G$ be a simple graph. An independent set is a set of pairwise non-adjacent vertices. The number of vertices in a maximum independent set of $G$ is denoted by $alpha(G)$. In this paper, we characterize graphs $G$ with $n$ vertices and with maximum
Tajedin Derikvand, Mohammad Reza Oboudi
doaj
Polynomial time recognition of vertices contained in all (or no) maximum dissociation sets of a tree
AIMS Mathematics, 2022 In a graph $ G $, a dissociation set is a subset of vertices which induces a subgraph with vertex degree at most 1. Finding a dissociation set of maximum cardinality in a graph is NP-hard even for bipartite graphs and is called the maximum dissociation ...
Jianhua Tu +3 more
doaj +1 more source
Fair Packing of Independent Sets [PDF]
, 2020 In this work we add a graph theoretical perspective to a classical problem of fairly allocating indivisible items to several agents. Agents have different profit valuations of items and we allow an incompatibility relation between pairs of items described in terms of a conflict graph.
Nina Chiarelli +5 more
openalex +3 more sources
Fair Representation by Independent Sets [PDF]
, 2017 For a hypergraph $H$ let $ (H)$ denote the minimal number of edges from $H$ covering $V(H)$. An edge $S$ of $H$ is said to represent {\em fairly} (resp. {\em almost fairly}) a partition $(V_1,V_2, \ldots, V_m)$ of $V(H)$ if $|S\cap V_i|\ge \lfloor\frac{|V_i|}{ (H)}\rfloor$ (resp. $|S\cap V_i|\ge \lfloor\frac{|V_i|}{ (H)}\rfloor-1$) for all $i \le m$.
Aharoni, Ron +6 more
openaire +2 more sources