Research in Math
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Sponsored by SIGMAA TAHSMTue, 02 Sep 2014 16:21:12 +0000en-UShourly1https://wordpress.org/?v=4.8.4Domination in Hexagonal Chess
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http://www.teaguemath.com/domination-in-hexagonal-chess/#respondSat, 12 Jul 2014 17:19:22 +0000http://www.teaguemath.com/?p=168Hexagonal Chess Final
]]>http://www.teaguemath.com/domination-in-hexagonal-chess/feed/0Three-Player Nim
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http://www.teaguemath.com/three-player-nim-2/#respondFri, 11 Jul 2014 18:54:15 +0000http://www.teaguemath.com/?p=1643-player Nim (Sammy and Kavi)
]]>http://www.teaguemath.com/three-player-nim-2/feed/0Passing Stones
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http://www.teaguemath.com/passing-stones/#respondFri, 11 Jul 2014 18:53:00 +0000http://www.teaguemath.com/?p=161Passing Stones (An, Chen, Liang)
]]>http://www.teaguemath.com/passing-stones/feed/0Positive Triangles
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http://www.teaguemath.com/positive-triangles/#respondFri, 11 Jul 2014 18:52:11 +0000http://www.teaguemath.com/?p=158Positive Triangle Game (S, W, A, P)
]]>http://www.teaguemath.com/positive-triangles/feed/0Initial Ideas for Research
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http://www.teaguemath.com/initial-ideas-for-research/#respondFri, 11 Jul 2014 18:30:59 +0000http://www.teaguemath.com/?p=143Radio Labling Ideas (Fall 1)
]]>http://www.teaguemath.com/initial-ideas-for-research/feed/0First Results
http://www.teaguemath.com/145/
http://www.teaguemath.com/145/#respondFri, 11 Jul 2014 18:22:16 +0000http://www.teaguemath.com/?p=145Radio Labling Investigations (Fall 2)
]]>http://www.teaguemath.com/145/feed/0Second Paper
http://www.teaguemath.com/147/
http://www.teaguemath.com/147/#respondFri, 11 Jul 2014 18:20:46 +0000http://www.teaguemath.com/?p=147Radio Labeling 2nd Paper
]]>http://www.teaguemath.com/147/feed/0Final Paper
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http://www.teaguemath.com/final-paper/#respondFri, 11 Jul 2014 18:10:49 +0000http://www.teaguemath.com/?p=150Radio Labeling (siemens)
]]>http://www.teaguemath.com/final-paper/feed/0Parity NIM
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Mon, 07 Oct 2013 23:38:01 +0000http://gibsonmath.com/research/?p=91Continue reading Parity NIM→]]>Parity NIM consists of a pile containing an odd number of objects from which players take turns removing one or more objects, with at most \(k\) objects removed by each player during his or her turn. The player who has removed an odd number of objects at the end of the game wins. If \(n\) is the number of objects in the initial pile, a specific solution for the pair \((n,k)\) can be found. However, no general solution is known.
]]>Partizen Graph Coloring
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Fri, 04 Oct 2013 21:32:43 +0000http://gibsonmath.com/research/?p=84Continue reading Partizen Graph Coloring→]]>Partizen Graph Coloring Game has two players: Alice and Bob. The players alternate coloring the uncolored vertices of a finite graph G from a fixed finite set of colors. At each step of the game, the players must choose to color an uncolored vertex with a legal color. In the basic formation of the game, a color is legal for an uncolored vertex if the vertex has no neighbors already colored with that color. Alice wins the game if all vertices of the graph are colored; otherwise, Bob wins. The least such that Alice has a winning strategy for this game on \(G\) is called the game chromatic number of G. If the definition of legal color is altered so that at each step in the game, each color class must have maximum degree at most \(d\), for some fixed integer \(dge{0}\), then the least such that Alice has a winning strategy is called the \(d\)-relaxed game chromatic number of \(G\). These parameters have been studied extensively for many classes of graphs. The classes for which the most is known are trees and forests. While upper bounds on the game chromatic number (and \(d\)-relaxed game chromatic number) are known for these classes, and the bounds are known to be achievable, it is not known what structural properties the graphs must have in order to achieve the bounds. This project will attempt to find these properties, thereby classifying these classes completely with respect to the Partizen Graph Coloring Game. We will then attempt to classify trees and forests relative to the d-relaxed game chromatic number for small values of \(d\). Finally, we may consider other variations of the game in which the definition of legal color is altered in other ways.
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