论文标题
图表匹配的新结果从保留度增长的学位
New results on graph matching from degree preserving growth
论文作者
论文摘要
最近引入的\ emph {度保留生长}模型（自然物理学，\ doi {10.1038/s41567-021-01417-7}）使用匹配项将规定的学位的新顶点插入到当前生长图序列的当前图中。该过程都取决于最大的可用匹配项的大小，这是我们在这里的重点以及匹配的实际选择。 首先，我们表明，以新的度量$2δ$扩展的图形度序列是否与序列实现中的可用匹配密切相关。也就是说，我们证明扩展问题等同于存在与大小$δ$匹配的原始度序列的实现。 其次，我们提出了度序列的\ emph {强制匹配数}的下限。该数字是学位序列的任何实现中最大匹配的大小。然后，我们研究序列的\ emph {某些}实现中最大匹配的大小，称为\ emph {势匹配数}。我们还估计了最大匹配和最大匹配的最小尺寸，由度序列确定，独立于图形实现。沿着这条线，我们回答了一个由Biedl提出的问题，Demaine \ Emph {et al。}（\ doi {10.1016/j.disc.2004.05.003}）。
The recently introduced \emph{Degree Preserving Growth} model (Nature Physics, \DOI{10.1038/s41567-021-01417-7}) uses matchings to insert new vertices of prescribed degrees into the current graph of an ever-growing graph sequence. The process depends both on the size of the largest available matchings, which is our focus here, as well as on the actual choice of the matching. First we show that the question whether a graphic degree sequence, extended with a new degree $2δ$ remains graphic is closely related to the available matchings in the realizations of the sequence. Namely we prove that the extension problem is equivalent to the existence of a realization of the original degree sequence with a matching of size $δ$. Second we present lower bounds for the \emph{forcible matching number} of degree sequences. This number is the size of the maximum matchings in any realization of the degree sequence. We then study bounds on the size of maximal matchings in \emph{some} realizations of the sequence, known as the \emph{potential matching number}. We also estimate the minimum size of both the maximal and the maximum matchings, as determined by the degree sequence, independently of graphical realizations. Along this line we answer a question raised by Biedl, Demaine \emph{et al.} (\DOI{10.1016/j.disc.2004.05.003}).
