论文标题
奇怪的着色，无冲突的着色和强烈的着色数字
Odd colourings, conflict-free colourings and strong colouring numbers
论文作者
论文摘要
奇数色数和无冲突的色度是Petruševski和škrekovski[2021]和Fabrici，Lužar，Rindošová和Soták[2022]引入的新图参数。在本说明中，我们显示具有限制性$ 2 $ -Strong着色号的图形具有有限的奇数色数和有限的无冲突色度数。这意味着具有有界扩展的图形类具有有限的奇数色数和有界的无冲突色数。此外，取决于已知的结果，即奇数色数和无冲突的$ k $ - 平面图的无冲突色数为$ o（k）$，这改善了Dujmović，Morin和Odak的最新结果[2022]。
The odd chromatic number and the conflict-free chromatic number are new graph parameters introduced by Petruševski and Škrekovski [2021] and Fabrici, Lužar, Rindošová and Soták [2022] respectively. In this note, we show that graphs with bounded $2$-strong colouring number have bounded odd chromatic number and bounded conflict-free chromatic number. This implies that graph classes with bounded expansion have bounded odd chromatic number and bounded conflict-free chromatic number. Moreover, it follows by known results that the odd chromatic number and the conflict-free chromatic number of $k$-planar graphs is $O(k)$ which improves a recent result of Dujmović, Morin and Odak [2022].
