AI 中文总结
研究图的色对称函数能否区分非同构单圈图，通过应用“三重删除”模关系，展示了一系列围长递增且具有相同色对称函数的非同构连通单圈图对，还给出首个具有相同色对称函数的无限二分图族。
AI 中文摘要
一个开放问题是图的色对称函数（CSF）是否能区分非同构树。已知CSF不能区分单圈图，但直到最近才知道存在围长大于3且具有相同CSF的单圈图对。本文展示了一系列非同构、连通、围长递增且具有相同CSF的单圈图对，还提供了首个具有相同CSF的无限二分图族。主要技术是应用“三重删除”模关系的一个版本，该版本由Guay-Paquet和Orellana--Scott分别独立提出。
英文摘要
An open question asks whether the chromatic symmetric function (CSF) of a graph distinguishes non-isomorphic trees. While it is known that the CSF does not distinguish unicyclic graphs, examples of pairs of unicyclic graphs with the same CSF and girth larger than 3 were not known until very recently. This manuscript exhibits a sequence of pairs of non-isomorphic, connected, unicyclic graphs with increasing girth and which share the same CSF. This also provides the first infinite family of bipartite graphs with the same CSF. Our main technique is to apply a version of the "triple deletion" modular relation, due independently to Guay-Paquet and Orellana--Scott.
Comments10 pages
