Large cliques or stable sets in graphs with no four-edge path and no five-edge path in the complement

2011 ◽  
Vol 70 (4) ◽  
pp. 449-472 ◽  
Author(s):  
Maria Chudnovsky ◽  
Yori Zwols
Keyword(s):  
Stable Sets ◽  
Edge Path

Covering Graphs by Colored Stable Sets

2004 ◽  
Vol 17 ◽  
pp. 145-149 ◽  
Author(s):  
Ulrich Faigle ◽  
Bernhard Fuchs ◽  
Britta Wienand
Keyword(s):  
Stable Sets

scholarly journals Coalition formation and history dependence

2020 ◽  
Vol 15 (1) ◽  
pp. 159-197 ◽  
Author(s):  
Bhaskar Dutta ◽  
Hannu Vartiainen
Keyword(s):  
Coalition Formation ◽  
Stable Set ◽  
Transferable Utility ◽  
Stable Sets ◽  
Solution Concepts ◽  
History Dependence ◽  
Von Neumann ◽  
Finite Games ◽  
A Chain ◽  
Indirect Dominance

Farsighted formulations of coalitional formation, for instance, by Harsanyi and Ray and Vohra, have typically been based on the von Neumann–Morgenstern stable set. These farsighted stable sets use a notion of indirect dominance in which an outcome can be dominated by a chain of coalitional “moves” in which each coalition that is involved in the sequence eventually stands to gain. Dutta and Vohra point out that these solution concepts do not require coalitions to make optimal moves. Hence, these solution concepts can yield unreasonable predictions. Dutta and Vohra restricted coalitions to hold common, history‐independent expectations that incorporate optimality regarding the continuation path. This paper extends the Dutta–Vohra analysis by allowing for history‐dependent expectations. The paper provides characterization results for two solution concepts that correspond to two versions of optimality. It demonstrates the power of history dependence by establishing nonemptyness results for all finite games as well as transferable utility partition function games. The paper also provides partial comparisons of the solution concepts to other solutions.

6. On the Way to Perfection: Primal Operations for Stable Sets in Graphs

2004 ◽  
pp. 51-76
Author(s):  
Claudio Gentile ◽  
Utz-Uwe Haus ◽  
Matthias Köppe ◽  
Giovanni Rinaldi ◽  
Robert Weismantel
Keyword(s):  
Stable Sets ◽  
The Way

scholarly journals Linial's Dual Conjecture for Path-Spine Digraphs

2020 ◽  
Author(s):  
Vinícius De Souza Carvalho ◽  
Cândida Nunes Da Silva ◽  
Orlando Lee
Keyword(s):  
Stable Sets ◽  
Hamilton Path ◽  
Directed Paths ◽  
Vertex Disjoint ◽  
Single Path

 Given a digraph D, a coloring 𝒞 of D is a partition of V(D) into stable sets. The k-norm of 𝒞 is defined as ΣC∈𝒞 min{|C|, k}. A coloring of D with minimum k-norm has its k-norm noted by χk(D). A (path)-k-pack of a digraph D is a set of k vertex-disjoint (directed) paths of D. The weight of a k-pack is the number of vertices covered by the k-pack. We denote by λk(D) the weight of a maximum k-pack. Linial conjectured that χk(D) ≤ λk(D) for every digraph. Such conjecture remains open, but has been proved for some classes of digraphs. We prove the conjecture for path-spine digraphs, defined as follows. A digraph D is path-spine if there exists a partition {X, Y} of V(D) such that D[X] has a Hamilton path and every arc in D[Y] belongs to a single path Q. 

scholarly journals Stable sets of planar homeomorphisms with translation pseudo-arcs

2019 ◽  
Vol 12 (8) ◽  
pp. 2379-2390 ◽  
Author(s):  
Francisco R. Ruiz del Portal ◽  
Keyword(s):  
Stable Sets
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