计数电路双盖

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-10-02 DOI:10.1002/jgt.23187

Radek Hušek, Robert Šámal

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引用次数: 0

摘要

研究了循环双盖猜想的一个计数版本。我们将讨论为什么计算电路更有趣(即，图同构于C k$ {C}_{k}$对于某些k$ k$)而不是循环（所有度为偶数的图）。我们给出了具有代表性的表面嵌入至少为4的图的近似指数下界。我们还证明了平面图的指数下界。我们推测任何无桥三次图至少有2n / 2−1 ${2}^{n/2-1}$电路双盖，我们给出了一个无限类图，这个图的界是紧的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Counting circuit double covers

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Counting circuit double covers

We study a counting version of Cycle Double Cover Conjecture. We discuss why it is more interesting to count circuits (i.e., graphs isomorphic to $C_{k}$ for some $k$ ) instead of cycles (graphs with all degrees even). We give an almost-exponential lower bound for graphs with a surface embedding of representativity at least 4. We also prove an exponential lower bound for planar graphs. We conjecture that any bridgeless cubic graph has at least $2^{n / 2 - 1}$ circuit double covers and we show an infinite class of graphs for which this bound is tight.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .