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AN n 5/2 ALGORITHM FOR MAXIMUM MATCHINGS IN BIPARTITE GRAPHS

by John E. Hopcroft, Richard M. Karp , 1973
"... 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)x/. ..."
Abstract - Cited by 702 (1 self) - Add to MetaCart
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)x/.

of bipartite graphs

by Alice M. Deana, Joan P. Hutchinsonb , 1994
"... iple ells 'e is fO'l~ tnd ~ is ..."
Abstract - Add to MetaCart
iple ells 'e is fO'l~ tnd ~ is

Treewidth of Chordal Bipartite Graphs

by T. Kloks, D. Kratsch - J. ALGORITHMS , 1992
"... Chordal bipartite graph are exactly those bipartite graph in which every cycle of length at least six has a chord. The treewidth of a graph G is the smallest maximum cliquesize among all chordal supergraphs of G decreased by one. We present a polynomial time algorithm for the exact computation of ..."
Abstract - Cited by 20 (6 self) - Add to MetaCart
Chordal bipartite graph are exactly those bipartite graph in which every cycle of length at least six has a chord. The treewidth of a graph G is the smallest maximum cliquesize among all chordal supergraphs of G decreased by one. We present a polynomial time algorithm for the exact computation

An Attractive Class of Bipartite Graphs

by Rodica Boliac, Vadim V. Lozin , 2001
"... In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs. ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.

Intrinsic knotting of bipartite graphs

by Sophy Huck, Miguel Manrique - Undergrad. Papers in Knot Theory
"... Abstract: We further identify and categorize intrinsically knotted bipartite graphs. We are motivated by a conjecture that a bipartite graph with E ≥ 4V- 17 is intrinsically knotted. We verify the conjecture for graphs that have exactly 6 vertices in one part and at least 6 in the other. We also pr ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
Abstract: We further identify and categorize intrinsically knotted bipartite graphs. We are motivated by a conjecture that a bipartite graph with E ≥ 4V- 17 is intrinsically knotted. We verify the conjecture for graphs that have exactly 6 vertices in one part and at least 6 in the other. We also

Bisimplicial edges in bipartite graphs

by Matthijs Bomhoff , Bodo Manthey - Discrete Appl. Math
"... Abstract Bisimplicial edges in bipartite graphs are closely related to pivots in Gaussian elimination that avoid turning zeroes into non-zeroes. We present a new deterministic algorithm to find such edges in bipartite graphs. The expected time complexity of our new algorithm is O n 2 log n on rando ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Abstract Bisimplicial edges in bipartite graphs are closely related to pivots in Gaussian elimination that avoid turning zeroes into non-zeroes. We present a new deterministic algorithm to find such edges in bipartite graphs. The expected time complexity of our new algorithm is O n 2 log n

Minimal universal bipartite graphs

by Vadim V. Lozin
"... A graph U is (induced)-universal for a class of graphs X if every member of X is contained in U as an induced subgraph. We study the problem of nding a universal graph with minimum number of vertices for various classes of bipartite graphs: exponential classes of bipartite (and general) graphs, bipa ..."
Abstract - Cited by 3 (2 self) - Add to MetaCart
A graph U is (induced)-universal for a class of graphs X if every member of X is contained in U as an induced subgraph. We study the problem of nding a universal graph with minimum number of vertices for various classes of bipartite graphs: exponential classes of bipartite (and general) graphs

Packing bipartite graphs with covers of complete bipartite graphs

by Jérémie Chalopin, Daniël Paulusma - Proc 7th Int Conf on Algorithms and Complexity, Lecture Notes in Computer Science , 2010
"... Abstract. For a set S of graphs, a perfect S-packing (S-factor) of a graph G is a set of mutually vertex-disjoint subgraphs of G that each are isomorphic to a member of S and that together contain all vertices of G. IfG allows a covering (locally bijective homomorphism) to a graph H, thenG is an H-c ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
-cover. For some fixed H let S(H) consist of all H-covers. Let Kk,ℓ be the complete bipartite graph with partition classes of size k and ℓ, respectively. For all fixed k, ℓ ≥ 1, we determine the computational complexity of the problem that tests if a given bipartite graph has a perfect S(Kk,ℓ)-packing. Our

Forbidden induced bipartite graphs

by Peter Allen - J. GRAPH THEORY , 2006
"... Given a fixed bipartite graph H, we study the asymptotic speed of growth of the number of bipartite graphs on n vertices which do not contain an induced copy of H. Whenever H contains either a cycle or the bipartite complement of a cycle, the speed of growth is 2 Ω(n 6 5). For every other bipartite ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
Given a fixed bipartite graph H, we study the asymptotic speed of growth of the number of bipartite graphs on n vertices which do not contain an induced copy of H. Whenever H contains either a cycle or the bipartite complement of a cycle, the speed of growth is 2 Ω(n 6 5). For every other bipartite

Edge-coloring in bipartite graphs

by Ajai Kapoor, Romeo Rizzi , 1997
"... Given a bipartite graph G with n nodes, m edges and maximum degree \Delta, we find an edge coloring for G using \Delta colors in time T + O(m log \Delta), where T is the time needed to find a perfect matching in a k-regular bipartite graph with at most O(m) edges and k ^ \Delta. Together with best k ..."
Abstract - Cited by 10 (1 self) - Add to MetaCart
Given a bipartite graph G with n nodes, m edges and maximum degree \Delta, we find an edge coloring for G using \Delta colors in time T + O(m log \Delta), where T is the time needed to find a perfect matching in a k-regular bipartite graph with at most O(m) edges and k ^ \Delta. Together with best
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