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Bootstrap clustering for graph partitioning∗

Philippe Gambette, Alain Guénoche (2012)

RAIRO - Operations Research

Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this profile,...

Borsuk-Ulam type theorems

Adam Idzik (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

A generalization of the theorem of Bajmóczy and Bárány which in turn is a common generalization of Borsuk's and Radon's theorem is presented. A related conjecture is formulated.

Bounded expansion in web graphs

Silvia Gago, Dirk Schlatter (2009)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study various models for web graphs with respect to bounded expansion. All the deterministic models even have constant expansion, whereas the copying model has unbounded expansion. The most interesting case turns out to be the preferential attachment model --- which we conjecture to have unbounded expansion, too.

Bounding neighbor-connectivity of Abelian Cayley graphs

Lynne L. Doty (2011)

Discussiones Mathematicae Graph Theory

For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighbor-connectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is bounded above by κ. Doty has sharpened that bound in abelian Cayley graphs to approximately (1/2)κ. The...

Bounds concerning the alliance number

Grady Bullington, Linda Eroh, Steven J. Winters (2009)

Mathematica Bohemica

P. Kristiansen, S. M. Hedetniemi, and S. T. Hedetniemi, in Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004), 157–177, and T. W. Haynes, S. T. Hedetniemi, and M. A. Henning, in Global defensive alliances in graphs, Electron. J. Combin. 10 (2003), introduced the defensive alliance number a ( G ) , strong defensive alliance number a ^ ( G ) , and global defensive alliance number γ a ( G ) . In this paper, we consider relationships between these parameters and the domination number γ ( G ) . For any positive integers...

Bounds for index of a modified graph

Bo Zhou (2004)

Discussiones Mathematicae Graph Theory

If a graph is connected then the largest eigenvalue (i.e., index) generally changes (decreases or increases) if some local modifications are performed. In this paper two types of modifications are considered: (i) for a fixed vertex, t edges incident with it are deleted, while s new edges incident with it are inserted; (ii) for two non-adjacent vertices, t edges incident with one vertex are deleted, while s new edges incident with the other vertex are inserted. ...

Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs

P. Francis, S. Francis Raj (2016)

Discussiones Mathematicae Graph Theory

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be a generalization...

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