Perfect graphs with polynomially computable kernels
نویسندگان
چکیده
منابع مشابه
Perfect graphs with polynomially computable kernels
In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a perfect graph. However, an open question is the complexity status of the computation of a kernel in such a digraph. Our main contribution is to prove new polyn...
متن کاملA note on kernels in h-perfect graphs
Boros and Gurvich [3] showed that every clique-acyclic superorientation of a perfect graph has a kernel. We prove the following extension of their result: if G is an h-perfect graph, then every clique-acyclic and odd-hole-acyclic superorientation of G has a kernel. We propose a conjecture related to Scarf’s Lemma that would imply the reverse direction of the Boros-Gurvich theorem without relyin...
متن کاملPerfect graphs, kernels, and cores of cooperative games
A kernel of a directed graph D is defined as an independent set which is reachable from each outside vertex by an arc. A graph G is called kernel-solvable if an orientation D of G has a kernel whenever each clique of G has a kernel in D. The notion of kernel-solvability has important applications in combinatorics, list coloring, and game theory. It turns out that kernel-solvability is equivalen...
متن کاملComputable Markov-perfect industry dynamics
We provide a general model of dynamic competition in an oligopolistic industry with investment, entry, and exit. To ensure that there exists a computationally tractable Markov perfect equilibrium, we introduce firm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. Our game of incomplete information always has an equilibrium in cutoff entry...
متن کاملAn Overview of Polynomially Computable Characteristics of Special Interval Matrices
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying polynomially solvable classes thus belongs to important current trends. The purpose of this paper is to review some of such classes. In particular, we focus on se...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2020
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.09.027