Year: 2026
Type: preprint
Abstract: A set S of vertices of a graph is odd independent if it is independent and every vertex outside S has either zero or an odd number of neighbors in S. The largest size of such a set is the odd independence number alpha_od. Caro, Petrusevski, Skrekovski and Tuza [2] conjectured that alpha_od = 1 for every finite Queen graph. They also asked whether the infinite Queen graph has alpha_od = 1 or alpha_od = infinity. We prove that alpha_od = 1 in both cases. In particular, in the case of an infinite board we prove that alpha_od = 1 holds on the quarter plane and on the whole plane.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Problémy teórie grafov súvisiace so vzdialenosťou, G1298066903, G1535239153, Metric properties of Graphs, Regulárne mapy: konštrukcie a klasifikácia, G3165774659, Výnimočné štruktúry v diskrétnej matematike: vlastnosti, konštrukcie a klasifikácie, G494568048, G5243991293, G5841098923, Grafy, mapy a dizajny s vysokým stupňom symetrie, G6873202014, G6948331134, G8088548421, G827957027, G8530662581
OpenAlex ID: W7203931825