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Element-Removal Games on Acyclic Graphs and Posets
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2015 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Elementborttagningsspel på acykliska grafer och pomängder (Swedish)
Abstract [en]

This paper is about element-removal games on acyclic graphs and posets. Two players alternate in turn by removing one element at a time according to the rules. If a player on her turn cannot make a move she loses and the game ends.

Here we give formulas for the game value of games on trees where the players are only allowed to remove leaves. We also show how to compute the game value of games on some posets whose Hasse diagram is cycle-free and the players must remove maximal and/or minimal elements.

Abstract [sv]

Denna uppsats handlar om elementbortagningsspel på acykliska grafer och pomängder. Två spelare turas om att ta bort element enligt reglerna. Spelet är slut när en spelare under sin tur inte kan göra ett drag och därmed förlorar.

Här ger vi formler för värdet för spel på träd där spelarna enbart får ta bort löv. Vi visar även hur man kan beräkna värdet för spel på pomängder vars Hassediagram är fritt från cykler och spelarna bara får ta bort maximala och/eller minimala element.

Place, publisher, year, edition, pages
2015.
Series
TRITA-MAT-E, 2015:86
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-178184OAI: oai:DiVA.org:kth-178184DiVA: diva2:882750
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2015-12-15 Created: 2015-12-07 Last updated: 2015-12-15Bibliographically approved

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  • apa
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