关于弹性图的着色
On Coloring Resilient Graphs
摘要：
我们引入了一个新的概念弹性约束满足问题，更精确地确定NP-硬度和弹性实例的有效算法的存在之间的边界的目标。特别地，我们研究了$r$ -弹性$k$ -可着色图，这些$k$ -可着色图即使在添加了任何$r$新边之后仍保持$k$ -可着色.证明了弹性可着色图着色的NP-硬度的下界，并给出了一个充分弹性图着色的算法。我们还分析了$k$ -SAT的相应弹性概念。弹性的概念为图着色和其他组合问题提出了一系列悬而未决的问题。
英文摘要：
We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study $r$-resiliently $k$-colorable graphs, which are those $k$-colorable graphs that remain $k$-colorable even after the addition of any $r$ new edges. We prove lower bounds on the NP-hardness of coloring resiliently colorable graphs, and provide an algorithm that colors sufficiently resilient graphs. We also analyze the corresponding notion of resilience for $k$-SAT. This notion of resilience suggests an array of open questions for graph coloring and other combinatorial problems.
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