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Complete bipartite graph

About: Complete bipartite graph is a research topic. Over the lifetime, 2753 publications have been published within this topic receiving 44422 citations. The topic is also known as: biclique.


Papers
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Journal ArticleDOI
TL;DR: This paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.
Abstract: The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.

2,785 citations

Proceedings ArticleDOI
13 Oct 1971
TL;DR: In this paper, a bipartite graph with n vertices and m edges was constructed in a number of computation steps proportional to (m+n) n, where n is the number of edges in the graph.
Abstract: The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m+n) n.

1,243 citations

01 Apr 1975
TL;DR: In this article, the authors generalize this result to arbitrary graphs, at the same time strengthening and simplifying the original bipartite result and showing that k-term arithmetic progression-free sets of integers must have density zero.
Abstract: : A crucial lemma in recent work of the author (showing that k-term arithmetic progression-free sets of integers must have density zero) stated (approximately) that any large bipartite graph can be decomposed into relatively few 'nearly regular' bipartite subgraphs. In this note the author generalizes this result to arbitrary graphs, at the same time strengthening and simplifying the original bipartite result.

1,151 citations

Journal ArticleDOI
TL;DR: A new extension of the primal-dual schema and the use of Lagrangian relaxation to derive approximation algorithms for the metric uncapacitated facility location problem and the metric k-median problem achieving guarantees of 3 and 6 respectively.
Abstract: We present approximation algorithms for the metric uncapacitated facility location problem and the metric k-median problem achieving guarantees of 3 and 6 respectively. The distinguishing feature of our algorithms is their low running time: O(m logm) and O(m logm(L + log (n))) respectively, where n and m are the total number of vertices and edges in the underlying complete bipartite graph on cities and facilities. The main algorithmic ideas are a new extension of the primal-dual schema and the use of Lagrangian relaxation to derive approximation algorithms.

872 citations

Book ChapterDOI
01 Jan 2001
TL;DR: In this article, the energy of a graph G is defined as the sum of the absolute values of the eigenvalues of G. The connection between E and the total electron energy of organic molecules is briefly outlined.
Abstract: Let G be a graph possessing n vertices and m edges. The energy of G, denoted by E = E(G), is the sum of the absolute values of the eigenvalues of G. The connection between E and the total electron energy of a class of organic molecules is briefly outlined. Some (known) fundamental mathematical results on E are presented: the relation between E(G) and the characteristic polynomial of G, lower and upper bounds for E, especially those depending on n and m, graphs extremal with respect to E, n-vertex graphs for which E(G) > E(K n ). The characterization of the n-vertex graph(s) with maximal value of E is an open problem.

604 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202341
202271
202193
2020106
201985
201897