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Bipartite subgraphs of integer weighted graphs

Noga Alon, Eran Halperin
1998 Discrete Mathematics  
For every 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).  ... 
doi:10.1016/s0012-365x(97)00041-1 fatcat:uwf5hmage5b2phdm7c6oj7t374

Optimum matchings in weighted bipartite graphs [article]

Carlos E. Valencia, Marcos C. Vargas
2014 arXiv   pre-print
Given an 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.  ... 
arXiv:1403.5606v1 fatcat:3ffdzoyu4rhnldqspctxxxqmai

A Graph-Theoretic Approach to a Class of Integer-Programming Problems

J. F. Desler, S. L. Hakimi
1969 Operations Research  
This paper presents an efficient algorithm for finding a minimum-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.  ... 
doi:10.1287/opre.17.6.1017 fatcat:u7txhwsowrfdticm2g3hnid75e

Finding a maximum-weight induced k-partite subgraph of an i-triangulated graph

Louigi Addario-Berry, W.S. Kennedy, Andrew D. King, Zhentao Li, Bruce Reed
2010 Discrete Applied Mathematics  
We exhibit a polynomial time algorithm for finding a maximum-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.  ... 
doi:10.1016/j.dam.2008.08.020 fatcat:xwhifomaafhatnitq4iby6tiha

Decomposing a graph into subgraphs with small components [article]

Rain Jiang, Kai Jiang, Minghui Jiang
2021 arXiv   pre-print
Given a 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.  ... 
arXiv:2110.00692v1 fatcat:iwriqxv3bffkzbpkjigezorhly

Vertex-Coloring 2-Edge-Weighting of Graphs [article]

Hongliang Lu, Qinglin Yu, Cun-Quan Zhang
2010 arXiv   pre-print
A k- edge-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.  ... 
arXiv:1007.1505v2 fatcat:csszro35bjfubmz6dmzuqq3dee

Research of NP-Complete Problems in the Class of Prefractal Graphs

Rasul Kochkarov
2021 Mathematics  
NP-complete problems in 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.  ... 
doi:10.3390/math9212764 fatcat:kitwgsxezvdhfahfz5lhyrt2ca

On the approximation of minimum cost homomorphism to bipartite graphs

Monaldo Mastrolilli, Arash Rafiey
2013 Discrete Applied Mathematics  
Finally, we obtain a 2-approximation algorithm when H is a subclass 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.  ... 
doi:10.1016/j.dam.2011.05.002 fatcat:kscduq7x6vadziclpjdccbogtu

On the Complexity of Dissociation Set Problems in Graphs

Yury Orlovich, Alexandre Dolgui, Gerd Finke, Valery Gordon, Frank Werner
2009 IFAC Proceedings Volumes  
A subset 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.  ... 
doi:10.3182/20090603-3-ru-2001.0071 fatcat:3r4kvcgpknfabmigzn3vptjd5e

Vertex-coloring 2-edge-weighting of graphs

Hongliang Lu, Qinglin Yu, Cun-Quan Zhang
2011 European journal of combinatorics (Print)  
A k-edge-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.  ... 
doi:10.1016/j.ejc.2010.08.002 fatcat:leeebtfio5a5riearhouwom6wu

1-subdivisions, fractional chromatic number and Hall ratio [article]

Zdeněk Dvořák and Patrice Ossona de Mendez and Hehui Wu
2020 arXiv   pre-print
The Hall ratio 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.  ... 
arXiv:1812.07327v2 fatcat:vqgotw2mvff4hn2scvsbna4pka

Irregular embeddings of multigraphs with fixed chromatic number

Michael S. Jacobson, Jenö Lehel
1995 Discrete Mathematics  
In this note we show that G has an embedding as an induced 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).  ... 
doi:10.1016/0012-365x(94)00042-h fatcat:acdmr3horffjzcq7q7dmwa7owa

Algorithms and Hardness Results for the Maximum Balanced Connected Subgraph Problem [article]

Yasuaki Kobayashi, Kensuke Kojima, Norihide Matsubara, Taiga Sone, Akihiro Yamamoto
2020 arXiv   pre-print
We also consider a 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  ... 
arXiv:1910.07305v4 fatcat:oeyswibnnbctlddgg7s5ql2ae4

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.  ... 

The local density of triangle-free graphs

Stephan Brandt
1998 Discrete Mathematics  
How dense can every induced 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  ... 
doi:10.1016/s0012-365x(97)00074-5 fatcat:2vag7redfjbntf4qbh2vrl6scq
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