On graphic elementary lifts of graphic matroids

Graphic Elementary Lift of Cographic Matroids

“…We show that the forbidden minors obtained by Mundhe et al [2] are the only minimal minors not in the class C 3 .…”

“…We denote F = {F * 7 , M * (K In this paper, we use the technique discovered by Mundhe et al [2] to find the excluded minors. The following lemmas are used to prove the main theorems.…”

“…From the definition of an elementary quotient and above lemma, N/a = Q F , F ∈ F. Thus, we need quotients of every F ∈ F to find excluded minors for the class C k , for k ≥ 2, Mundhe et al [2] obtained graphic quotients for every F ∈ F as follows.…”

“…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. Let C k be the collection of cographic matroid whose splitting using k elements is graphic.…”

“…Case (i) If the quotient is graphic. In[2], Mundhe et al obtained forbidden minors from graphic quotients of every F ∈ F, as given in Theorem 1.1. Case (ii) If the quotient is not graphic.…”