独立数为2的图中的奇子式或奇浸入
Odd minors or odd immersions in graphs with independence number two
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中文总结 AI 辅助
针对独立数为2的图，在Kühn等人反驳奇Hadwiger猜想的背景下，证明这类图必包含K_{⌈n/2⌉}作为奇子式或全奇浸入，完善了相关图论结论。
中文摘要 AI 辅助
Kühn、Sauermann、Steiner和Wigderson近期反驳了奇Hadwiger猜想，即便对于独立数为2的图类也成立。对于该类图，该猜想等价于：每个含n个顶点且独立数为2的图G，都包含K_{⌈n/2⌉}作为奇子式。尽管这一结论不成立，我们证明每个独立数为2的图G，都包含K_{⌈n/2⌉}作为奇子式或全奇浸入。
英文摘要
Kühn, Sauermann, Steiner and Wigderson recently disproved the Odd Hadwiger Conjecture, even for graphs with independence number 2. For this class of graphs the conjecture is known to be equivalent to the following: every $n$-vertex graph $G$ with independence number 2 contains $K_{\lceil \frac n2 \rceil}$ as an odd minor. While this does not hold, we prove that every graph $G$ with independence number 2 contains $K_{\lceil \frac n2 \rceil}$ as an odd minor or as a totally odd immersion.
