37 citations · 38 across the 18 of their papers we have counts for
19 papers · 1 filter
Deduction with moves
Andrea C. Burgess, Nancy E. Clarke, Shannon L. Fitzpatrick +1
The deduction game may be thought of as a variant on the classical game of cops and robber in which the cops (searchers) aim to capture an invisible robber (evader); each cop is al…
Minimal Graph Embeddings via Point Deletions in Steiner triple systems
Melissa A. Huggan, Svenja Huntemann, Brett Stevens
The game Nofil is a two-player combinatorial game in which players take turns marking points of a design such that the set of marked points does not contain a block. Equivalently,…
A note on the strength of a hypercube
Melissa A. Huggan, M. E. Messinger, Dylan Pearson
As a generalization of super magic strength, the strength of a graph was introduced in [R. Ichishima, F.A. Muntaner-Batle, A. Oshima, Bounds for the strength of graphs, Austral. J.…
Cops and Attacking Robbers with Cycle Constraints
Alexander Clow, Melissa A. Huggan, M. E. Messinger
This paper considers the Cops and Attacking Robbers game, a variant of Cops and Robbers, where the robber is empowered to attack a cop in the same way a cop can capture the robber.…
Tic-Tac-Toe on Designs
Peter Danziger, Melissa A. Huggan, Rehan Malik +1
We consider playing the game of Tic-Tac-Toe on block designs BIBD() and transversal designs TD(). Players take turns choosing points and the first player to complete…
The damage number of the Cartesian product of graphs
Melissa A. Huggan, Margaret-Ellen Messinger, Amanda Porter
We consider a variation of Cops and Robber, introduced in [D. Cox and A. Sanaei, The damage number of a graph, [Aust. J. of Comb. 75(1) (2019) 1-16] where vertices visited by a rob…
The localization capture time of a graph
Natalie C. Behague, Anthony Bonato, Melissa A. Huggan +2
The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the locatio…
The combinatorial game nofil played on Steiner Triple Systems
Melissa A. Huggan, Svenja Huntemann, Brett Stevens
We introduce an impartial combinatorial game on Steiner triple systems called Nofil. Players move alternately, choosing points of the triple system. If a player is forced to fill a…
Progress on the localization number of a graph
Anthony Bonato, Melissa A. Huggan, Trent G. Marbach
We highlight new results on the localization number of a graph, a parameter derived from the localization graph searching game. After introducing the game and providing an overview…
The game of Flipping Coins
Anthony Bonato, Melissa A. Huggan, Richard J. Nowakowski
We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by…
An investigation into the application of genetic programming to combinatorial game theory
Melissa A. Huggan, Craig Tennenhouse
Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and sol…
A Note on Numbers
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
When are all positions of a game numbers? We show that two properties are necessary and sufficient. These properties are consequences of that, in a number, it is not an advantage t…
Ordinal Sums, Clockwise Hackenbush, and Domino Shave
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
We present two rulesets, Domino Shave and Clockwise Hackenbush. The first is somehow natural and, as special cases, includes Stirling Shave and Hetyei's Bernoulli game. Clockwise H…
Tic-Tac-Toe on an Affine Plane of order 4
Peter Danziger, Melissa A. Huggan, Rehan Malik +1
The game of tic-tac-toe is well known. In particular, in its classic version it is famous for being unwinnable by either player. While classically it is played on a grid, it is nat…
The localization number and metric dimension of graphs of diameter 2
Anthony Bonato, Melissa A. Huggan, Trent Marbach
We consider the localization number and metric dimension of certain graphs of diameter , focusing on families of Kneser graphs and graphs without 4-cycles. For the Kneser graphs…
Cops and an Insightful Robber
Melissa A. Huggan, Richard J. Nowakowski
The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observe…
Cheating Robot Games: A model for insider information
Melissa A. Huggan, Richard J. Nowakowski
Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. Thes…
The localization number of designs
Anthony Bonato, Melissa A. Huggan, Trent Marbach
We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via d…
Simultaneous Combinatorial Game Theory
Melissa Huggan, Richard J. Nowakowski, Paul Ottaway
Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no cha…