Relaxation procedures on graphs

Authors:
Elias Wegert;Christian Reiher
Affiliations:
Institute of Applied Analysis, TechUniv Freiberg, Germany;Keble College, University of Oxford, UK,
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 6
Cited 1

Refelection sequences

American Mathematical Monthly
Reflection processes on graphs and Weyl groups

Journal of Combinatorial Theory Series A
Some combinatorial problems

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Reachability is decidable in the numbers game

Theoretical Computer Science
The numbers game and Coxeter groups

Proceedings of the 4th conference on Formal power series and algebraic combinatorics
Strong convergence and a game of numbers

European Journal of Combinatorics

Chip-firing games, potential theory on graphs, and spanning trees

Journal of Combinatorial Theory Series A

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Abstract

The procedures studied in this paper originate from a problem posed at the International Mathematical Olympiad in 1986. We present several approaches to the IMO problem and its generalizations. In this context we introduce a ''signed mean value procedure'' and study ''relaxation procedures on graphs''. We prove that these processes are always finite, thus confirming a conjecture of Akiyama, Hosono and Urabe [J. Akiyama, K. Hosono, M. Urabe, Some combinatorial problems. Discrete Mathematics 116 (1993) 291-298]. Moreover, we indicate relations to sorting and to an iterative method used in circle packing.