Mathematics Faculty Publications
Document Type
Article
Publication Date
1-8-2025
Disciplines
Discrete Mathematics and Combinatorics | Mathematics
Abstract
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the set. The convex hull of a set of vertices is the smallest convex set containing the set. We study variations of two games introduced by Buckley and Harary, where two players take turns selecting previously-unselected vertices of a graph until the convex hull of the jointly-selected vertices becomes too large. The last player to move is the winner. The achievement game ends when the convex hull contains every vertex. In the avoidance game, the convex hull is not allowed to contain every vertex. We determine the nim-value of these games for several graph families.
Copyright Statement
This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00182-024-00916-0
Recommended Citation
Benesh BJ, Ernst DC, Meyer M, Salmon SK, Sieben N. 2025 Impartial geodetic building games on graphs. International Journal of Game Theory. 53: 1335–1368. https://doi.org/10.1007/s00182-024-00916-0
