2023/03/03 by Gunjal, Sachin, Jagadale, Uday, Malavadkar, Prashant
#05B35 #05C50 #05C83 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2303.01898
In this paper, we define generalized splitting and element splitting operations on p-matroids. p-matroids are the matroids representable over GF(p). The circuits and the bases of the new matroid are characterized in terms of circuits and bases of the original matroid, respectively. A class of n-connected p-matroids which gives n-connected p- matroids using the generalized splitting operation is also characterized. We also prove that connectivity of p-matroid is preserved under element splitting operation. Sufficient conditions to obtain Eulerian p-matroid from Eulerian p-matroid under splitting and element splitting operations are provided.