2-边连通无三角超欧拉图的研究

doi:10.13371/j.cnki.chin.q.j.m.2026.02.006

数学季刊 ›› 2026, Vol. 41 ›› Issue (2): 174-183.doi: 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

School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China

收稿日期:2025-10-12 出版日期:2026-06-30 发布日期:2026-06-30
作者简介: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.
基金资助:
Supported by 2025 Natural Science Foundation of Qinghai Province (Grant No. 2025-ZJ-902T).

2-Edge Connected Triangle-Free Supereulerian Graphs

School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China

Received:2025-10-12 Online:2026-06-30 Published:2026-06-30
About author: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.
Supported by:
Supported by 2025 Natural Science Foundation of Qinghai Province (Grant No. 2025-ZJ-902T).

摘要/Abstract

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

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

中图分类号:

O157.6

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.

LV Sheng-mei, MA Xing-zhong, ZHOU Dan. 2-Edge Connected Triangle-Free Supereulerian Graphs[J]. Chinese Quarterly Journal of Mathematics, 2026, 41(2): 174-183.

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[3]	郑洁, 刘朝阳. 图上的随机动力系统及其诱导的马尔可夫链[J]. 数学季刊, 2008, 23(2): 207-214.

2-边连通无三角超欧拉图的研究

2-Edge Connected Triangle-Free Supereulerian Graphs

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