关于屋形图与一条边被细分一次的K₄图共性的初等证明
Elementary Proofs of Commonality of the House Graph and $K_4$ with One Edge Subdivided
AI总结：
本研究针对屋形图与一条边被细分一次的K₄图，给出了无需旗代数的初等证明，证明二者均为共性图，回应了相关学者对“易于人类理解”证明的需求。
摘要：
若在大完全图的2-边着色中，每种颜色占比相等的随机着色能渐近最小化图H的单色拷贝数，则称H为共性图。已有研究通过旗代数方法证明屋形图与一条边被细分一次的K₄图是共性图，Grzesik、Lee、Lidický和Volec要求给出这两个图共性的“易于人类理解”的证明。本短文给出了无需旗代数的证明，表明这两个图均为共性图。
英文摘要：
A graph $H$ is called common if the number of monochromatic copies of $H$ in a $2$-edge-coloring of a large complete graph is asymptotically minimized by the random coloring with an equal proportion of each color. The house graph and $K_4$ with one edge subdivided once are known to be common by the flag algebra method. Grzesik, Lee, Lidický, and Volec asked for ``human-friendly'' proofs of the commonality of these two graphs. In this short note, we give flag-algebra-free proofs that both graphs are common.
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。
