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Subdivisions in a bipartite graph

Authors: Balbuena Martínez, Maria Camino Teófila; Cera, Martín; García-Vázquez, Pedro; Valenzuela, Juan Carlos;

Subdivisions in a bipartite graph

Abstract

Given a bipartite graph G with m and n vertices, respectively,in its vertices classes, and given two integers s, t such that 2 ≤ s ≤ t, 0 ≤ m−s ≤ n−t, and m+n ≤ 2s+t−1, we prove that if G has at least mn−(2(m−s)+n−t) edges then it contains a subdivision of the complete bipartite $K_(s,t)$ with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn − (2(m − s) + n − t + 1) edges for this topological Turan type problem.

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Spain
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Keywords

Graph theory, Combinatorial analysis, Grafs, Teoria de, Classificació AMS::05 Combinatorics::05C Graph theory, :05 Combinatorics::05C Graph theory [Classificació AMS], Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs, Bipartite graphs, Anàlisi combinatòria, :Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs [Àrees temàtiques de la UPC]

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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