关于强性和鲁棒性临界图
On strongly and robustly critical graphs
AI总结：
本文提出鲁棒k-临界图的概念，并证明通过将临界图与足够大的完全图连接可得到鲁棒临界图。
摘要：
在极值组合学中，通常关注那些在某种性质下最小的结构。特别是，临界图和列表临界图在图着色理论中占据重要地位。Stiebitz、Tuza和Voigt引入了强临界图，即那些在k-临界性下却对任意非常数列表分配L（大小为k-1）可着色的图。在这里，我们强化这一概念，并将其扩展到DP着色（或对应着色）的框架中，通过定义鲁棒k-临界图：这些图不是(k-1)-DP着色的，但仅仅是因为χ(G)=k。然后我们寻求构造鲁棒临界图的一般方法。我们的主要结果是，如果G是一个临界图（相对于普通着色），则将G与足够大的完全图连接后，得到的图是鲁棒临界图；这一结果甚至对于强临界性也是新的。
英文摘要：
In extremal combinatorics, it is common to focus on structures that are minimal with respect to a certain property. In particular, critical and list-critical graphs occupy a prominent place in graph coloring theory. Stiebitz, Tuza, and Voigt introduced strongly critical graphs, i.e., graphs that are $k$-critical yet $L$-colorable with respect to every non-constant assignment $L$ of lists of size $k-1$. Here we strengthen this notion and extend it to the framework of DP-coloring (or correspondence coloring) by defining robustly $k$-critical graphs as those that are not $(k-1)$-DP-colorable, but only due to the fact that $χ(G) = k$. We then seek general methods for constructing robustly critical graphs. Our main result is that if $G$ is a critical graph (with respect to ordinary coloring), then the join of $G$ with a sufficiently large clique is robustly critical; this is new even for strong criticality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
