On the characterization of Eulerian $es$-splitting $p$-matroids
Abstract
The -splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over called -matroids, the -splitting operation may yield Eulerian matroids. In this work, we introduce the -splitting operation for -matroids and characterize a class of -matroids yielding Eulerian matroids after the -splitting operation. Characterization of circuits, and bases of the resulting matroid, after the -splitting operation, in terms of circuits, and bases of the original matroid, respectively, are discussed. We also proved that the -splitting operation on -matroids preserves connectivity and 3-connectedness. Sufficient condition to obtain Hamiltonian -matroid from Hamiltonian -matroid under -splitting operation is also provided.
Keywords
Cite
@article{arxiv.2205.03180,
title = {On the characterization of Eulerian $es$-splitting $p$-matroids},
author = {Uday Jagadale and Prashant Malavadkar and Sachin Gunjal and M. M. Shikare},
journal= {arXiv preprint arXiv:2205.03180},
year = {2022}
}