Max k-cutChromatic numberLargest eigenvaluesLargest Laplacian eigenvalueSmallest adjacency eigenvalueLet G be a graph of order n and size m, and let mck (G) be the maximum size of a k-cut of G. It is shown thatNikiforov, V.Linear Algebra and its Applications...
Max k-cut Chromatic number Largest eigenvalues Largest Laplacian eigenvalue Smallest adjacency eigenvalue 1. Introduction and main results The maximum k-cut of G, denoted by mck(G), is the maximum number of edges in a k-partite subgraph of G. This note provides an upper bound on mck(G) ...
An instance of the max k −cut game is an edge weighted graph. Every vertex is controlled by an autonomous agent with strategy space [1..k]. Given a player i, his payoff is defined as the total weight of the edges [i,j] such that pl
[1] in two directions: to biased partitions, and to partitions into k≥3 parts. In Section 2, we give results on biased partitions. For p∈[0,1] and q=1−p, define mp(G)=minV(G)=V1∪.V2qe(V1)+pe(V2). Note that this is a ‘biased’ generalization of Max Cut: if we ...
improved approximation algorithms for max k-cut and max对于max k-cut最大改进的近似算法 系统标签: cut max approximation algorithms improved goemans ImprovedApproximationAlgorithmsforMAXk-CUTandMAXBISECTIONAlanFrieze∗CarnegieMellonUniversityMarkJerrum†UniversityofEdinburghJune1994;revisedJune1995AbstractPolynom...
We consider a capacitated max k -cut problem in which a set of vertices is partitioned into k subsets. Each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that maximizes the...
We consider the MAX k -CUT problem on random graphs G n , p . First, we bound the probable weight of a MAX k -CUT using probabilistic counting arguments and by analyzing a simple greedy heuristic. Then, we give an algorithm that approximates MAX k -CUT in expected polynomial time, wit...
The Connected Max-k-Cut Problem is an extension of the well-known Max-Cut Problem. The objective is to partition a graph into k connected subgraphs by maximizing the cost of inter-partition edges. We propose a new integer linear program for the problem and a branch-and-cut algorithm. We ...
An approximation algorithm for hypergraph max k-cut with given sizes of parts - Ageev, SviridenkoA.A. Ageev and M.I. Sviridenko, “An approximation algorithm for Hypergraph Max k -Cut with given sizes of parts,” Lecture Notes in Computer Science (Proceedings of ESA'2000) , vol. 1879, ...
The standard parameterization of the Max-Cut problem sets the parameter to be the size k of the cut being sought. This turns out to be not very interesting for the following reason: Let m be the number of edges in the input graph G. By an early result of Erdős [7], we know that...