Abstract
For integers l and k with l > 0 and k > 0, let \({{\fancyscript{C}}(l, k)}\) denote the family of 2-edge-connected graphs G such that for each bond cut |S| ≤ 3, each component of G − S has at least (|V(G)| − k)/l vertices. In this paper we prove that if \({G\in {\fancyscript{C}}(7, 0)}\) , then G is not supereulerian if and only if G can be contracted to one of the nine specified graphs. Our result extends some earlier results (Catlin and Li in J Adv Math 160:65–69, 1999; Broersma and Xiong in Discrete Appl Math 120:35–43, 2002; Li et al. in Discrete Appl Math 145:422–428, 2005; Li et al. in Discrete Math 309:2937–2942, 2009; Lai and Liang in Discrete Appl Math 159:467–477, 2011).
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Bondy J.A., Murty U.S.R.: Graph Theory with Applications. American Elsevier, New York (1976)
Broersma H.J., Xiong L.: A note on minimun degree conditions for supereulerian graphs. Discrete Appl. Math. 120, 35–43 (2002)
Catlin P.A.: A reduction method to find spanning eulerian subgraphs. J. Graph Theory 12, 29–45 (1998)
Catlin P.A., Han Z.Y., Lai H.-J.: Graphs without spanning closed trails. Discrete Math. 160, 81–91 (1996)
Catlin P.A., Li X.: Supereulerian graphs of minimum degree at least 4. J. Adv. Math. 160, 65–69 (1999)
Jaeger F.: A note on sub-Eulerian graphs. J. Graph Theory 3, 91–93 (1979)
Lai H.-J., Liang Y.: Supereulerian graphs in the graph family C 2(6, k). Discrete Appl. Math. 159, 467–477 (2011)
Li D., Lai H.-J., Zhan M.: Eulerian subgraphs and Hamilton-connected line graphs. Discrete Appl. Math. 145, 422–428 (2005)
Li X., Li D., Lai H.-J.: The supereulerian graphs in the graph family C(l, k). Discrete Math. 309, 2937–2942 (2009)
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Xiangwen Li was supported by the Natural Science Foundation of China (11171129). Liming Xiong was supported by the Natural Science Fundation of China (11071016).
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Li, X., Wang, C., Fan, Q. et al. Spanning Eulerian Subgraphs of 2-Edge-Connected Graphs. Graphs and Combinatorics 29, 275–280 (2013). https://doi.org/10.1007/s00373-011-1108-0
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DOI: https://doi.org/10.1007/s00373-011-1108-0