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<p>In this paper, we first show that Eulerian-minors, constructed from Eulerian subgraphs through edge contractions, preserve Eulerian properties and establish a well-quasi-ordering under the Eulerian-minor relation. Then we concisely characterize Eulerian, planar, and outer-planar Eulerian graphs by excluding Eulerianminors. Furthermore, we introduce a novel planar operation that generates all 4-regular planar graphs from a bouquet consisted of two loops. This significantly simplifies prior methods proposed by Manca and Lehel for generating simple 4-regular planar graphs.</p>

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Eulerian-minors and Recursive Characterization of 4-regular Planar Graphs

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Metrose Metsidik,
  • Qi Yan

摘要

In this paper, we first show that Eulerian-minors, constructed from Eulerian subgraphs through edge contractions, preserve Eulerian properties and establish a well-quasi-ordering under the Eulerian-minor relation. Then we concisely characterize Eulerian, planar, and outer-planar Eulerian graphs by excluding Eulerianminors. Furthermore, we introduce a novel planar operation that generates all 4-regular planar graphs from a bouquet consisted of two loops. This significantly simplifies prior methods proposed by Manca and Lehel for generating simple 4-regular planar graphs.