2-Edge Connected Triangle-Free Supereulerian Graphs

LV Sheng-mei, MA Xing-zhong, ZHOU Dan

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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