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Bipartite subgraphs of integer weighted graphs

1998
*
Discrete Mathematics
*

For every

doi:10.1016/s0012-365x(97)00041-1
fatcat:uwf5hmage5b2phdm7c6oj7t374
*integer*p > 0, let f(p) be the minimum possible value*of*the maximum*weight**of*a cut in an*integer**weighted**graph*with total*weight*p. ... This supplies the precise value*of*f(p) for many values*of*p including, e.g., all p = (i) ÷ (~) when n is large enough and ~ml 2 ~< 5n.' ... Thus, f(p) is the largest*integer*such that any*integer*-*weighted**graph*with total*weight*p contains a*bipartite**subgraph*with total*weight*not less than f(p). ...##
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Optimum matchings in weighted bipartite graphs
[article]

2014
*
arXiv
*
pre-print

Given an

arXiv:1403.5606v1
fatcat:3ffdzoyu4rhnldqspctxxxqmai
*integer**weighted**bipartite**graph*{G=(U V, E), w:E→Z} we consider the problems*of*finding all the edges that occur in some minimum*weight*matching*of*maximum cardinality and enumerating all the ... Moreover, we construct a*subgraph*G_cs*of*G which depends on an ϵ-optimal solution*of*the dual linear program associated to the assignment problem on {G,w} that allows us to reduced this problems to their ... Introduction Given an*integer**weighted**bipartite**graph*{G, w}, that is, a*bipartite**graph*G = (U ⊔ V, E) with*bipartitions*U and V and an*integer**weight*function w : E → Z over the edges*of*G. ...##
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A Graph-Theoretic Approach to a Class of Integer-Programming Problems

1969
*
Operations Research
*

This paper presents an efficient algorithm for finding a minimum-

doi:10.1287/opre.17.6.1017
fatcat:u7txhwsowrfdticm2g3hnid75e
*weight*generalized matching in a*weighted**bipartite**graph*. ... Finally, the paper gives an algorithm that applies the same concept to a*graph*that is not necessarily*bipartite*. ... For the case where the*graph*is*bipartite*, it can be shown that the problem*of*finding a minimum-*weight*feasible*subgraph*is equivalent to the HITCHCOCK [8] problem*of**integer*programming. ...##
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Finding a maximum-weight induced k-partite subgraph of an i-triangulated graph

2010
*
Discrete Applied Mathematics
*

We exhibit a polynomial time algorithm for finding a maximum-

doi:10.1016/j.dam.2008.08.020
fatcat:xwhifomaafhatnitq4iby6tiha
*weight*induced k-partite*subgraph**of*an i-triangulated*graph*, and show that the problem*of*finding a maximum-size*bipartite*induced*subgraph*... A*graph*is clique-separable precisely if every induced*subgraph*either has a clique cutset, or is a complete multipartite*graph*or a clique joined to an arbitrary*bipartite**graph*. ... For a fixed positive*integer*k we formally define MWIKS as follows: Maximum-*weight*k-partite*subgraph*Instance: A*graph*G with*weight*function w : V (G) → Z + and a positive*integer*l. ...##
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Decomposing a graph into subgraphs with small components
[article]

2021
*
arXiv
*
pre-print

Given a

arXiv:2110.00692v1
fatcat:iwriqxv3bffkzbpkjigezorhly
*graph*G and two*integers*k and c, (k,c)-Decomposition is the problem*of*deciding whether G admits an edge partition into k*subgraphs*with component size at most c. ... The component size*of*a*graph*is the maximum number*of*edges in any connected component*of*the*graph*. ... 3/2 in*bipartite**graphs*. ...##
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Vertex-Coloring 2-Edge-Weighting of Graphs
[article]

2010
*
arXiv
*
pre-print

A k- edge-

arXiv:1007.1505v2
fatcat:csszro35bjfubmz6dmzuqq3dee
*weighting*w*of*a*graph*G is an assignment*of*an*integer**weight*, w(e)∈{1,..., k}, to each edge e. ... In particular, we show that 3-connected*bipartite**graphs*admit vertex-coloring 2-edge-*weighting*. ... A k-edge-*weighting*w*of*a*graph*G is an assignment*of*an*integer**weight*w(e) ∈ {1, . . . , k} to each edge e*of*G. ...##
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Research of NP-Complete Problems in the Class of Prefractal Graphs

2021
*
Mathematics
*

NP-complete problems in

doi:10.3390/math9212764
fatcat:kitwgsxezvdhfahfz5lhyrt2ca
*graphs*, such as enumeration and the selection*of**subgraphs*with given characteristics, become especially relevant for large*graphs*and networks. ... We propose a class*of*prefractal*graphs*and review particular statements*of*NP-complete problems. As an example, algorithms for searching for spanning trees and packing*bipartite**graphs*are proposed. ... Conflicts*of*Interest: The author declares no conflict*of*interest. ...##
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On the approximation of minimum cost homomorphism to bipartite graphs

2013
*
Discrete Applied Mathematics
*

Finally, we obtain a 2-approximation algorithm when H is a subclass

doi:10.1016/j.dam.2011.05.002
fatcat:kscduq7x6vadziclpjdccbogtu
*of*doubly convex*bipartite**graphs*that has as special case*bipartite*nets and tents. Crown ... For a fixed target*graph*H, the minimum cost homomorphism problem, MinHOM(H), asks, for a given*graph*G with*integer*costs c i (u), u ∈ V (G), i ∈ V (H), and an*integer*k, whether or not there exists a ... If the target*bipartite**graph*H has the*bipartite*claw as an induced*subgraph*then the integrality gap*of*the LP described in Section 2 can be arbitrarily large. Proof. ...##
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On the Complexity of Dissociation Set Problems in Graphs

2009
*
IFAC Proceedings Volumes
*

A subset

doi:10.3182/20090603-3-ru-2001.0071
fatcat:3r4kvcgpknfabmigzn3vptjd5e
*of*vertices in a*graph*is called a dissociation set if it induces a*subgraph*with vertex degree at most 1. A dissociation set D is maximal if no other dissociation set contains D. ... The complexity*of*finding a dissociation set*of*maximum size in line*graphs*and finding a maximal dissociation set*of*minimum size in general*graphs*is considered. ... An example*of**graph** G is shown in Fig. 3 . Assign to each vertex*of** G in ) (G V the*weight*1 and to each*of*the remaining vertices*of** G the*weight*2. Then the following statement holds. ...##
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Vertex-coloring 2-edge-weighting of graphs

2011
*
European journal of combinatorics (Print)
*

A k-edge-

doi:10.1016/j.ejc.2010.08.002
fatcat:leeebtfio5a5riearhouwom6wu
*weighting*w*of*a*graph*G is an assignment*of*an*integer**weight*, w(e) ∈ {1, . . . , k}, to each edge e. ... In particular, we show that 3-connected*bipartite**graphs*admit vertex-coloring 2edge-*weighting*. ... A k-edge-*weighting*w*of*a*graph*G is an assignment*of*an*integer**weight*w(e) ∈ {1, . . . , k} to each edge e*of*G. ...##
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1-subdivisions, fractional chromatic number and Hall ratio
[article]

2020
*
arXiv
*
pre-print

The Hall ratio

arXiv:1812.07327v2
fatcat:vqgotw2mvff4hn2scvsbna4pka
*of*a*graph*G is the maximum*of*|V(H)|/alpha(H) over all*subgraphs*H*of*G. Clearly, the Hall ratio*of*a*graph*is a lower bound for the fractional chromatic number. ... c > 0, every*graph**of*sufficiently large average degree contains as a*subgraph*the 1-subdivision*of*a*graph**of*fractional chromatic number at least c. * For every d > 0, there exists a*graph*G*of*average ... We would like to thank the reviewers, whose suggestions helped us improve the presentation*of*the paper. ...##
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Irregular embeddings of multigraphs with fixed chromatic number

1995
*
Discrete Mathematics
*

In this note we show that G has an embedding as an induced

doi:10.1016/0012-365x(94)00042-h
fatcat:acdmr3horffjzcq7q7dmwa7owa
*subgraph*, into some degree irregular c-chromatic multigraph having the same maximum edge multiplicity. * Corresponding author. ... An immediate corollary*of*Theorem 3 (with c = 2) is a result or irregular embedding*of**bipartite**graphs*communicated in [1, Theorem 11]. ... It is a natural question to look for irregular c-chromatic host*graphs**of*maximum edge multiplicity s with minimum order n = n(c, s). ...##
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Algorithms and Hardness Results for the Maximum Balanced Connected Subgraph Problem
[article]

2020
*
arXiv
*
pre-print

We also consider a

arXiv:1910.07305v4
fatcat:oeyswibnnbctlddgg7s5ql2ae4
*weighted*version*of*BCS (WBCS). ... The goal is to find a maximum connected*subgraph**of*G having the same number*of*blue vertices and red vertices. ... We also consider a*weighted*counterpart*of*BCS, namely WBCS: the input is vertex-*weighted*bicolored*graph*and the goal is to find a maximum*weight*connected*subgraph*H in which the total*weights**of*red ...##
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Page 3542 of Mathematical Reviews Vol. , Issue 93g
[page]

1993
*
Mathematical Reviews
*

Consider a

*weighted**graph*G in which each edge has*weight*w(e) > 0 and define the*weight**of*a*subgraph*H*of*G by w(H) = Dece(H) W(e). ... Let G(X, Y,£) denote a*bipartite**graph*G with edge set E and a*bipartition*{X,Y}*of*the vertex set V(G) such that |X| =|Y| = n> 2. ...##
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The local density of triangle-free graphs

1998
*
Discrete Mathematics
*

How dense can every induced

doi:10.1016/s0012-365x(97)00074-5
fatcat:2vag7redfjbntf4qbh2vrl6scq
*subgraph**of*L:~nJ vertices (0<c~<l)*of*a triangle-free*graph**of*order n be? ... Moreover, the local density will be related to a long-standing conjecture*of*Erdrs, saying that every triangle-free*graph*can be made*bipartite*by the omission*of*at most n2/25 edges. ... Wilbrink for pointing out that //41 is a quartic residue*graph*, Barbara Baumeister for helpful discussions concerning strongly regular*graphs*, and several people at our department, who helped me to overcome ...
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