Basis pair graphs of transversal matroids are connected
The basis pair graph of a matroid on the ground set S has, as its vertices, ordered triples of the form \((B_ 1,B_ 2,B_ 3)\), where \(B_ 1\) and \(B_ 2\) are disjoint bases and \(B_ 3=S\setminus (B_ 1\cup B_ 2)\). Two such vertices, \((A_ 1,A_ 2,A_ 3)\) and \((B_ 1,B_ 2,B_ 3)\), are adjacent if \((B_ 1,B_ 2,B_ 3)\) can be obtained from \((A_ 1,A_ 2,A_ 3)\) by interchanging two elements of S belonging to different components of \((A_ 1,A_ 2,A_ 3)\). It is known that basis pair graphs of graphic and cographic matroids are connected. We show that this holds for transversal matroids as well.
scientific article; zbMATH DE number 4083683
scientific article