Displaying similar documents to “On a sphere of influence graph in a one-dimensional space”

Erdös-Ko-Rado from intersecting shadows

Gyula O.H. Katona, Ákos Kisvölcsey (2012)

Discussiones Mathematicae Graph Theory

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A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results.

Some news about the independence number of a graph

Jochen Harant (2000)

Discussiones Mathematicae Graph Theory

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For a finite undirected graph G on n vertices some continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the independence number of G.

Spaces of ω-limit sets of graph maps

Jie-Hua Mai, Song Shao (2007)

Fundamenta Mathematicae

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Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.

On a generalization of the friendship theorem

Mohammad Hailat (2012)

Discussiones Mathematicae Graph Theory

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The Friendship Theorem states that if any two people, of a group of at least three people, have exactly one friend in common, then there is always a person who is everybody's friend. In this paper, we generalize the Friendship Theorem to the case that in a group of at least three people, if every two friends have one or two common friends and every pair of strangers have exactly one friend then there exist one person who is friend to everybody in the group. In particular, we show that...