发表机构
Slovak University of Technology in Bratislava; University of Split; University of Novo mesto; University of Ljubljana; Rudolfovo – Science and Technology Centre Novo mesto（布拉迪斯拉发斯洛伐克理工大学; 斯普利特大学; 新梅斯托大学; 卢布尔雅那大学; Rudolfovo——新梅斯托科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明有限皇后图的奇独立数为1，同时解决了无限皇后图奇独立数的猜想与疑问，得出无限皇后图在四分之一平面及整个平面上的奇独立数也为1的结论。
AI 中文摘要
图的顶点集S若满足独立且S外的每个顶点在S中的邻居数为0或奇数，则称S为奇独立集，这类集合的最大规模称为奇独立数α_od。Caro、Petrusevski、Skrekovski与Tuza[2]猜想，所有有限皇后图的α_od=1，同时他们询问无限皇后图的α_od是1还是无穷大。本文证明有限与无限皇后图的α_od均为1，特别地，对于无限棋盘，本文证明四分之一平面及整个平面上的皇后图均满足α_od=1。
英文摘要
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.
Comments10 pages, 2 figures
