有界度图的最大权重二等分下界
Lower Bounds for Maximum Weight Bisections of Graphs with Bounded Degrees
AI总结：
本文研究有界最大度边加权图的最大权重二等分，改进已有无权图下界，并将3-正则图的紧界推广到加权次立方及无三角形情形。
摘要：
图中的二等分是一种割，其中两个部分的顶点数相差至多1。本文给出了最大度有界的边加权图中二等分最大权重的下界。对于最大度为偶数或等于3的图，以及几乎所有图，我们的结果改进了Lee、Loh和Sudakov（J. Comb. Th. Ser. B 103 (2013)）关于（无权）最大二等分的界。我们证明，Bollobás和Scott（J. Graph Th. 46 (2004)）得到的3-正则图中最大二等分规模的紧下界可以推广到加权次立方图。我们还考虑了边加权无三角形次立方图，并证明对此类图存在远优于边加权次立方图的下界，尤其是在排除$K_{1,3}$时。我们提出了三个猜想。
英文摘要：
A bisection in a graph is a cut in which the number of vertices in the two parts differ by at most 1. In this paper, we give lower bounds for the maximum weight of bisections of edge-weighted graphs with bounded maximum degree. Our results improve a bound of Lee, Loh, and Sudakov (J. Comb. Th. Ser. B 103 (2013)) for (unweighted) maximum bisections in graphs whose maximum degree is either even or equals 3, and for almost all graphs. We show that a tight lower bound for maximum size of bisections in 3-regular graphs obtained by Bollobás and Scott (J. Graph Th. 46 (2004)) can be extended to weighted subcubic graphs. We also consider edge-weighted triangle-free subcubic graphs and show that a much better lower bound (than for edge-weighted subcubic graphs) holds for such graphs especially if we exclude $K_{1,3}$. We pose three conjectures.
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。
