数学季刊 >

2026 , Vol. 41 >Issue 2: 174 - 183

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2026.02.006

2-边连通无三角超欧拉图的研究

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  • School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China
LV Sheng-mei (1980-), female, native of Xining, Qinghai, professor of Qinghai Minzu University, Ph.D, engages in graph theory; MA Xing-zhong (1999-), male, native of Minhe, Qinghai, master of Qinghai Minzu University, engages in graph theory; ZHOU Dan (2000-), female, native of Xianyang, Shaanxi, master of Qinghai Minzu University, engages in graph theory.
LV Sheng-mei (1980-), female, native of Xining, Qinghai, professor of Qinghai Minzu University, Ph.D, engages in graph theory;

收稿日期: 2025-10-12

  网络出版日期: 2026-06-30

基金资助

Supported by 2025 Natural Science Foundation of Qinghai Province (Grant No. 2025-ZJ-902T).

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2-Edge Connected Triangle-Free Supereulerian Graphs

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  • School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China
LV Sheng-mei (1980-), female, native of Xining, Qinghai, professor of Qinghai Minzu University, Ph.D, engages in graph theory; MA Xing-zhong (1999-), male, native of Minhe, Qinghai, master of Qinghai Minzu University, engages in graph theory; ZHOU Dan (2000-), female, native of Xianyang, Shaanxi, master of Qinghai Minzu University, engages in graph theory.
LV Sheng-mei (1980-), female, native of Xining, Qinghai, professor of Qinghai Minzu University, Ph.D, engages in graph theory;

Received date: 2025-10-12

  Online published: 2026-06-30

Supported by

Supported by 2025 Natural Science Foundation of Qinghai Province (Grant No. 2025-ZJ-902T).

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摘要

In 2-connected Hamiltonian claw-free graphs involving degree sum of adjacent vertices [Discuss. Math. Graph Theory 40(2020) 85-106 [24]], Tian and Xiong proved that 2-edge connected triangle-free graph of order at most 7 is either supereulerian or one of G1. Furthermore, in Edge degree conditions for dominating and spanning closed trails
[Discuss. Math. Graph Theory 44(2024) 363-381 [23]], Tian, Broersma and Xiong proved that 2-edge connected graph of order at most 8 is either supereulerian or one of G1∪G2. Motivated by the advance above, we considered 2-edge connected graph G of order at most 9, and show that G is either supereulerian or one of G1∪G2∪G3. Although only one vertex is added, forbidden graphs are more complex and harder to derived.

关键词： Hamilton cycle; Supereulerian graph; Spanning closed trail; Dominating closed trail

本文引用格式

吕盛梅, 马兴忠, 周丹 . 2-边连通无三角超欧拉图的研究[J]. 数学季刊, 2026 , 41(2) : 174 -183 . DOI: 10.13371/j.cnki.chin.q.j.m.2026.02.006

Abstract

In 2-connected Hamiltonian claw-free graphs involving degree sum of adjacent vertices [Discuss. Math. Graph Theory 40(2020) 85-106 [24]], Tian and Xiong proved that 2-edge connected triangle-free graph of order at most 7 is either supereulerian or one of G1. Furthermore, in Edge degree conditions for dominating and spanning closed trails
[Discuss. Math. Graph Theory 44(2024) 363-381 [23]], Tian, Broersma and Xiong proved that 2-edge connected graph of order at most 8 is either supereulerian or one of G1∪G2. Motivated by the advance above, we considered 2-edge connected graph G of order at most 9, and show that G is either supereulerian or one of G1∪G2∪G3. Although only one vertex is added, forbidden graphs are more complex and harder to derived.

Key words： Hamilton cycle; Supereulerian graph; Spanning closed trail; Dominating closed trail

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