由抛物线引起的完全图$K_{p+1}$的一分解

Q4 Mathematics

Theory and Applications of Graphs Pub Date : 2022-01-01 DOI:10.20429/tag.2022.090202

G. Kiss, Nicola Pace, A. Sonnino

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引用次数: 0

摘要

AG(2, q)中有三种类型的仿射正多边形:椭圆、双曲线和抛物线。前两种情况已经在以前的论文中进行了调查。本文构造并详细描述了由抛物线产生的完全图Kn的一类特殊几何一分解。在计算机辅助研究的支持下，我们还推测，直到同构，这是唯一的单因子分解，其中每个单因子要么由一条线表示，要么由一条抛物线表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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One-factorizations of the complete graph $K_{p+1}$ arising from parabolas

There are three types of affine regular polygons in AG(2, q): ellipse, hyperbola and parabola. The first two cases have been investigated in previous papers. In this note, a particular class of geometric one-factorizations of the complete graph Kn arising from parabolas is constructed and described in full detail. With the support of computer aided investigation, it is also conjectured that up to isomorphisms this is the only one-factorization where each one-factor is either represented by a line or a parabola.

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来源期刊

Theory and Applications of Graphs Mathematics-Discrete Mathematics and Combinatorics

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

20 weeks