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math.CO2021★ 1 cited
A chain theorem for sequentially -rank-connected graphs with respect to vertex-minors
Duksang Lee, Sang-il Oum
Tutte (1961) proved the chain theorem for simple -connected graphs with respect to minors, which states that every simple -connected graph has a simple -connected mino…
math.CO2021★ 1 cited
Intertwining connectivities for vertex-minors and pivot-minors
Duksang Lee, Sang-il Oum
We show that for pairs and of disjoint subsets of vertices of a graph , if is sufficiently large, then there exists a vertex in $V(G)-(Q\cup R\cup S\cup…
math.CO2020
Characterizing matroids whose bases form graphic delta-matroids
Duksang Lee, Sang-il Oum
We introduce delta-graphic matroids, which are matroids whose bases form graphic delta-matroids. The class of delta-graphic matroids contains graphic matroids as well as cographic…