A modular approach to Sprouts

Sprouts is a two players game that was first introduced by M.S. Patterson and J.H. Conway in 1967. There are two players A and B that, starting from a set of x 0 vertices, build a graph by alternatively connecting any two vertices with degree less than three with an edge, and by drawing a new vertex...

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Published inDiscrete Applied Mathematics Vol. 144; no. 3; pp. 303 - 319
Main Authors Focardi, Riccardo, Luccio, Flaminia L.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Lausanne Elsevier B.V 15.12.2004
Amsterdam Elsevier
New York, NY
Subjects
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Game theory
Games
Graph theory
Mathematics
Operational research and scientific management
Operational research. Management science
Planar graphs
Sciences and techniques of general use
Theoretical computing
Algorithms
Planar graphs
Games
Drawing
Computer theory
Planar graph
Combinatorics
Algorithm
Game theory
Optimization
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2003.11.008

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Abstract Sprouts is a two players game that was first introduced by M.S. Patterson and J.H. Conway in 1967. There are two players A and B that, starting from a set of x 0 vertices, build a graph by alternatively connecting any two vertices with degree less than three with an edge, and by drawing a new vertex on this new edge. A move is allowed only if the new connection maintains the planarity of the graph. The player that executes the last possible move is the winner. We study some new topological properties of this game and we show their effectiveness by giving a complete analysis of the case x 0=7 for which, to the best of our knowledge, no formal proof has been previously given.
AbstractList Sprouts is a two players game that was first introduced by M.S. Patterson and J.H. Conway in 1967. There are two players A and B that, starting from a set of x 0 vertices, build a graph by alternatively connecting any two vertices with degree less than three with an edge, and by drawing a new vertex on this new edge. A move is allowed only if the new connection maintains the planarity of the graph. The player that executes the last possible move is the winner. We study some new topological properties of this game and we show their effectiveness by giving a complete analysis of the case x 0=7 for which, to the best of our knowledge, no formal proof has been previously given.
Author Luccio, Flaminia L.
Focardi, Riccardo
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  surname: Luccio
  fullname: Luccio, Flaminia L.
  email: luccio@dsm.univ.trieste.it
  organization: Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy
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10.1038/scientificamerican0767-112
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Keywords Algorithms
Planar graphs
Games
Drawing
Computer theory
Planar graph
Combinatorics
Algorithm
Game theory
Optimization
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Nushizeki (10.1016/j.dam.2003.11.008_BIB10) 1988
References_xml – reference: E.R. Berlekamp, J.H. Conway, R.K. Guy, Winning Ways for your Mathematical Plays, Vol. 2: Games in Particular, Academic Press, New York, 1982, pp. 564–568 (Chapter 17).
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SubjectTerms Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Exact sciences and technology
Game theory
Games
Graph theory
Mathematics
Operational research and scientific management
Operational research. Management science
Planar graphs
Sciences and techniques of general use
Theoretical computing
Title A modular approach to Sprouts
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