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Bipartite subgraphs of integer weighted graphs
1998
Discrete Mathematics
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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]
2014
arXiv
pre-print
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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
1969
Operations Research
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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
2010
Discrete Applied Mathematics
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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]
2021
arXiv
pre-print
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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]
2010
arXiv
pre-print
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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
2021
Mathematics
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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
2013
Discrete Applied Mathematics
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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
2009
IFAC Proceedings Volumes
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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
2011
European journal of combinatorics (Print)
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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]
2020
arXiv
pre-print
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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
1995
Discrete Mathematics
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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]
2020
arXiv
pre-print
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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
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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
1998
Discrete Mathematics
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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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