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On a MinMax Theorem of Cacti
, 1997
"... A simple proof is presented for the minmax theorem of Lov'asz on cacti. Instead of using the result of Lov'asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem. 1 Introduction The graph matching problem and the matroid intersection problem ..."
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A simple proof is presented for the minmax theorem of Lov'asz on cacti. Instead of using the result of Lov'asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem. 1 Introduction The graph matching problem and the matroid intersection
A MinMax Theorem on Tournaments
"... We present a structural characterization of all tournaments T = (V, A) such that, for any nonnegative integral weight function defined on V, the maximum size of a feedback vertex set packing is equal to the minimum weight of a triangle in T. We also answer a question of Frank by showing that it is ..."
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We present a structural characterization of all tournaments T = (V, A) such that, for any nonnegative integral weight function defined on V, the maximum size of a feedback vertex set packing is equal to the minimum weight of a triangle in T. We also answer a question of Frank by showing that it is NPcomplete to decide whether the vertex set of a given tournament can be partitioned into two feedback vertex sets. In addition, we give exact and approximation algorithms for the feedback vertex set packing problem on tournaments.
A Uniform MinMax Theorem with Applications in Cryptography
, 2013
"... We present a new, more constructive proof of von Neumann’s MinMax Theorem for twoplayer zerosum game — specifically, an algorithm that builds a nearoptimal mixed strategy for the second player from several bestresponses of the second player to mixed strategies of the first player. The algorithm ..."
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We present a new, more constructive proof of von Neumann’s MinMax Theorem for twoplayer zerosum game — specifically, an algorithm that builds a nearoptimal mixed strategy for the second player from several bestresponses of the second player to mixed strategies of the first player. The algorithm
MinMax theorem about the Road Coloring Conjecture
 DMTCS PROC., AE
, 2005
"... The Road Coloring Conjecture is an old and classical conjecture posed in Adler and Weiss (1970); Adler et al. (1977). Let G be a strongly connected digraph with uniform outdegree 2. The Road Coloring Conjecture states that, under a natural (necessary) condition that G is “aperiodic”, the edges of G ..."
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of coloring we prove our generalized MinMax theorem. Using the Prime Number Theorem (PNT) we further show that the number of colors needed for each edge is bounded above by O(log n / log log n), where n is the number of vertices in the digraph.
On approximate minmax theorems of graph connectivity problems
, 2006
"... Given an undirected graph G and a subset of vertices S ` V (G), we call the vertices in S the terminal vertices and the vertices in V (G) S the Steiner vertices. In this thesis, we study two problems whose goals are to achieve high "connectivity " among the terminal vertices. The ..."
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arcdisjoint paths to each terminal vertex in D. Both problems are generalizations of two classical graph theoretical problems: the edgedisjoint s, tpaths problem and the edgedisjoint spanning trees problem. Polynomial time algorithms and exact minmax relations are known for the classical problems
A Multiplayer Generalization of the MinMax Theorem
"... We show that in zerosum polymatrix games, a multiplayer generalization of twoperson zerosum games, Nash equilibria can be found efficiently with linear programming. We also show that the set of coarse correlated equilibria collapses to the set of Nash equilibria. In contrast, other positive prope ..."
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properties of twoperson zerosum games are not preserved: Nash equilibrium payoffs need not be unique, and Nash equilibrium strategies need not be exchangeable or maxmin.
Generalized Skew Bisubmodularity: A Characterization and a MinMax Theorem
, 2013
"... Huber, Krokhin, and Powell (Proc. SODA2013) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the threevalue domain. In this paper we consider a natural generalization of the c ..."
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of the concept of skew bisubmodularity and show a connection between the generalized skew bisubmodularity and a convex extension over rectangles. We also analyze the dual polyhedra, called skew bisubmodular polyhedra, associated with generalized skew bisubmodular functions and derive a minmax theorem
MINMAX THEOREMS RELATED TO GEOMETRIC REPRESENTATIONS OF GRAPHS AND THEIR SDPS
, 2010
"... We prove a simple nonlinear identity relating the Lovász theta number of a graph to its smallest radius hypersphere embedding where each edge has unit length. We use this identity and its generalizations to establish minmax theorems and to translate results related to one of the graph invariants ..."
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We prove a simple nonlinear identity relating the Lovász theta number of a graph to its smallest radius hypersphere embedding where each edge has unit length. We use this identity and its generalizations to establish minmax theorems and to translate results related to one of the graph invariants
Approximate MinMax Theorems for Steiner RootedOrientations of Graphs and Hypergraphs
, 2006
"... Given an undirected hypergraph and a subset of vertices S ⊆ V with a specified root vertex r ∈ S, the Steiner RootedOrientation problem is to find an orientation of all the hyperedges so that in the resulting directed hypergraph the “connectivity” from the root r to the vertices in S is maximized. ..."
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. This is motivated by a multicasting problem in undirected networks as well as a generalization of some classical problems in graph theory. The main results of this paper are the following approximate minmax relations: • Given an undirected hypergraph H, if S is 2khyperedgeconnected in H, then H has a Steiner
Results 1  10
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