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Pure Mathematics 2026
关于图笛卡尔积和子式的注记
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Abstract:
设
和
分别表示图
和
的笛卡尔积和字典积。本文研究了图积中的子式问题。特别地,我们通过构造方法证明,对任意简单图
和连通图
,图
是图
的一个子式,其中
是
的
重笛卡尔积且
。这一结论推广了Wood的早期结果。此外,我们还改进了Wood中
的下界,其中
。
Let
and
denote the Cartesian product and the lexicographic product of graphs
and
, respectively. In this note, we investigate the graph minor in products of graphs. In particular, we show that, for any simple graph
and any connected graph
, the graph
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