Cycles containing all the odd-degree vertices

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Cycles containing all the odd-degree vertices

机译：包含所有奇数顶点的循环

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The number of cycles in a graph containing any fixed edge and also containing all vertices of odd degree is odd if and only if all vertices have even degree. If all vertices have even degree this is a theorem of Shunichi Toida. If all vertices have odd degree it is Andrew Thomason's extension of Smith's theorem. (C) 2019 Elsevier Inc. All rights reserved.

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《Journal of Combinatorial Theory, Series B》 |2020年第2020期|共7页
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Parity theorem; Hamiltonian cycle; Eulerian graph; Lifting a vertex;

机译：奇偶定理;哈密顿循环;欧拉图;举一个顶点;

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专利

1. Cycles containing all the odd-degree vertices [J] . Journal of Combinatorial Theory, Series B . 2020,第期

机译：包含所有奇数顶点的循环
2. On degree sum conditions for long cycles and cycles through specified vertices [J] . Tomoki Yamashita Discrete mathematics . 2008,第24期

机译：在长周期和经过指定顶点的周期的度和条件下
3. Disjoint cycles in hypercubes with prescribed vertices in each cycle [J] . Lin C.-K., Tan J.J.M., Hsu L.-H., Discrete Applied Mathematics . 2013,第18期

机译：超立方体的不相交周期，每个周期具有指定的顶点
4. Parity Linkage and the Erdos-Posa Property of Odd Cycles Through Prescribed Vertices in Highly Connected Graphs [C] . Felix Joos International workshop on graph-theoretic concepts in computer science . 2016

机译：高连通图中奇点的奇偶链接和奇数周期的鄂尔多斯-波萨性质
5. Displaced Vertices: A Search for Long-Lived Particles at CMS [D] . Quach, Dan. 2020

机译：移位顶点：在CMS上搜索长寿粒子
6. Neutral Rhenadicarbaboranes with Re(CO)2(NO) Vertices: A Theoretical Study of Building Blocks for Rhenacarborane-Based Drug Delivery Agents [O] . Amr A. A. Attia, Alexandru Lupan, Radu Silaghi-Dumitrescu, 2020

机译：具有Re（CO）2（NO）顶点的中性Rhenadicarbaboranes：基于Rhenacarborane的药物递送剂构建基的理论研究
7. Covering vertices by a specified number of disjoint cycles, edges and isolated vertices [O] . Chiba Shuya, Fujita Shinya 2013

机译：按指定数量的不连续循环，边线和孤立顶点覆盖顶点
8. Long Cycles in 2-Connected Graphs Containing All Vertices of Large Degree [R] . Trommel, H. 1996

机译：包含所有大度顶点的2连通图中的长周期

Cycles containing all the odd-degree vertices

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