论文标题
进一步的进步朝着哈德威格的猜想的列表和奇数版本
Further Progress towards the List and Odd Versions of Hadwiger's Conjecture
论文作者
论文摘要
1943年，哈德威格（Hadwiger）猜想，每张无$ k_t $ binor的图形都是$（t-1）$ - 每$ t \ ge 1 $可着色。在1980年代，Kostochka和Thomason独立证明了每个无$ k_t $ binor的图表的平均度$ O（t \ sqrt {\ log t}）$，因此为$ O（t \ sqrt {\ log log t}）$ - 可着色。最近，Song和作者Norin表明，每张无$ k_t $ binor的图形为$ O（t（\ log t）^β）$ - 每$β> 1/4 $可着色，从而根据$ o（t \ sqrt {\ log t}）的数量级进行第一个改进。在这项工作的基础上，我们以前证明了每个没有$ k_t $ binor的图形为$ o（t（\ log t）^β）$ - 每$β> 0 $都可以色彩。更具体地说，它们是$ o（t \ cdot（\ log \ log t）^{6}）$ - 可着色。在本文中，我们将这项工作扩展到了Hadwiger猜想的列表和奇怪的概括。
In 1943, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t\ge 1$. In the 1980s, Kostochka and Thomason independently proved that every graph with no $K_t$ minor has average degree $O(t\sqrt{\log t})$ and hence is $O(t\sqrt{\log t})$-colorable. Recently, Norin, Song and the author showed that every graph with no $K_t$ minor is $O(t(\log t)^β)$-colorable for every $β> 1/4$, making the first improvement on the order of magnitude of the $O(t\sqrt{\log t})$ bound. Building on that work, we previously showed that every graph with no $K_t$ minor is $O(t (\log t)^β)$-colorable for every $β> 0$. More specifically, they are $O(t \cdot (\log \log t)^{6})$-colorable. In this paper, we extend that work to the list and odd generalizations of Hadwiger's conjecture.
