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Builder-Blocker general position games | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 مرداد 1403 اصل مقاله (462.52 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29122.1854 | ||
| نویسندگان | ||
| Sandi Klavzar1، 2، 3؛ Jing Tian4، 2؛ James Tuite* 5 | ||
| 1Faculty of Mathematics and Physics, University of Ljubljana, Slovenia | ||
| 2Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia | ||
| 3Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia | ||
| 4School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, P.R. China | ||
| 5School of Mathematics and Statistics, Open University, Milton Keynes, UK | ||
| چکیده | ||
| This paper considers a game version of the general position problem in which a general position set is built through adversarial play. Two players in a graph, Builder and Blocker, take it in turns to add a vertex to a set, such that the vertices of this set are always in general position. The goal of Builder is to create a large general position set, whilst the aim of Blocker is to frustrate Builder's plans by making the set as small as possible. The game finishes when no further vertices can be added without creating three-in-a-line and the number of vertices in this set is the game general position number. We determine this number for some common graph classes and provide sharp bounds, in particular for the case of trees. We also discuss the effect of changing the order of the players. | ||
| کلیدواژه‌ها | ||
| general position set؛ games on graphs؛ trees؛ no-three-in-line؛ universal line | ||
| مراجع | ||
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