有界度图中下界附近的独立集
Independent sets near the lower bound in bounded degree graphs
摘要：
根据Brook定理，每个最大度不超过Delta = 3且团数不超过Delta的n-顶点图都是Delta-可染的，因而它有一个大小至少为n/Delta的独立集.我们给出了独立数接近这个界的图的一个近似刻画，并利用它证明了判定这样一个图是否有一个大小至少为n/Delta+k的独立集的问题有一个大小为O（k）的核.
英文摘要：
By Brook's Theorem, every n-vertex graph of maximum degree at most Delta >= 3 and clique number at most Delta is Delta-colorable, and thus it has an independent set of size at least n/Delta. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an indepdendent set of size at least n/Delta+k has a kernel of size O(k).
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。
