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The es-splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over \(GF(p),(p>2),\) called p-matroids, the es-splitting operation may yield Eulerian matroids. In this work, we introduce es-splitting operation for p-matroids and characterize a class of p-matroids yielding Eulerian matroids after the es-splitting operation. Characterization of circuits, and bases of the resulting matroid, after the es-splitting operation, in terms of circuits, and bases of the original matroid, respectively, are discussed. We also proved that the es-splitting operation on p-matroids preserves connectivity and 3-connectedness. Sufficient condition to obtain Hamiltonian p-matroid from Hamiltonian p-matroid under es-splitting operation is also provided.

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On the Characterization of Eulerian es-Splitting p-Matroids

  • 会议论文

  • 发表日期：

    2025年

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  • Uday Jagadale,
  • Sachin Gunjal,
  • Prashant Malavadkar,
  • M. M. Shikare,
  • B. N. Waphare

摘要

The es-splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over \(GF(p),(p>2),\) called p-matroids, the es-splitting operation may yield Eulerian matroids. In this work, we introduce es-splitting operation for p-matroids and characterize a class of p-matroids yielding Eulerian matroids after the es-splitting operation. Characterization of circuits, and bases of the resulting matroid, after the es-splitting operation, in terms of circuits, and bases of the original matroid, respectively, are discussed. We also proved that the es-splitting operation on p-matroids preserves connectivity and 3-connectedness. Sufficient condition to obtain Hamiltonian p-matroid from Hamiltonian p-matroid under es-splitting operation is also provided.