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Directed forests with application to algorithms related to Markov chains

Piotr Pokarowski (1999)

Applicationes Mathematicae

This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.

Domination Game: Extremal Families for the 3/5-Conjecture for Forests

Michael A. Henning, Christian Löwenstein (2017)

Discussiones Mathematicae Graph Theory

In the domination game on a graph G, the players Dominator and Staller alternately select vertices of G. Each vertex chosen must strictly increase the number of vertices dominated. This process eventually produces a dominating set of G; Dominator aims to minimize the size of this set, while Staller aims to maximize it. The size of the dominating set produced under optimal play is the game domination number of G, denoted by γg(G). Kinnersley, West and Zamani [SIAM J. Discrete Math. 27 (2013) 2090-2107]...

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