Graphic splitting of cographic matroids

Pirouz, Naiyer

doi:10.7151/dmgt.1782

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2023

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Cited by 2 publications

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“…Thus, the splitting operation does not protect matroid properties like graphicness, cographicness, etc. N. Pirouz [7] characterized a cographic matroid whose splitting using two elements is graphic. In the following theorem, Ganesh et al [2] characterized graphic matroid whose splitting matroid, using three elements, is graphic.…”

Section: Introductionmentioning

confidence: 99%

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Graphic Elementary Lift of Cographic Matroids

Solanki¹,

Mundhe²,

Dhotre³

2023

Preprint

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A matroid N is a lift of a binary matroid M , if N = Q\X when Q/X = M for some binary matroid Q and X ⊆ E(Q) and is called an elementary lift of M , if |X| = 1. A splitting operation on a binary matroid can result in an elementary lift. An elementary lift of a cographic or a graphic matroid need not be cographic or graphic. We intend to characterize the cographic matroids whose elementary lift is a graphic matroid.

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Section: Introductionmentioning

confidence: 99%

“…Theorem 1.2. [7] Let C be a cographic binary matroid, then C ∈ C 2 if and only if it does not have M(G 1 ) or M(G 2 ) minor, Figure 2 shows the graphs G 1 and G 2 .…”

Section: Introductionmentioning

confidence: 99%

Graphic Elementary Lift of Cographic Matroids

Solanki¹,

Mundhe²,

Dhotre³

2023

Preprint

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On graphic splitting of regular matroids

Mundhe¹,

Dalvi²

2020

Preprint

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Raghunathan at al. [9] introduced splitting operation with respect to a pair of element for binary matroid and characterized Eulerian binary matroids using it. In general, the splitting operation does not preserve the graphicness property of the given matroids. Shikare and Waphare [10] obtained the characterization for the class of graphic matroids which yield graphic matroids under the splitting operation with respect to a pair of elements. We study the effect of the splitting operation on regular matroids and characterize the class of regular matroids which yield graphic matroids under the splitting operation. We also provide an alternate and short proof to two of the known results.

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Graphic splitting of cographic matroids

Cited by 2 publications

References 3 publications

Graphic Elementary Lift of Cographic Matroids

Graphic Elementary Lift of Cographic Matroids

On graphic splitting of regular matroids

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