The basis exchange axiom has been a driving force in the development of matroid theory. In our recent paper titled Exchange distance of basis pairs in split matroids, we study the distance of basis pairs of a matroid in terms of symmetric exchanges. In particular, we give an upper bound on the minimum number of…
Our paper titled Hypergraph characterization of split matroids is now available on arXiv. The paper studies the structure of split matroids from a combinatorial point of view. We introduce the notion of elementary split matroids and give a hypergraph characterization in terms of independent sets. The proposed class is closed not only under duality and…
In a recent paper titled Inverse optimization problems with multiple weight functions, we introduce a new class of inverse optimization problems in which an input solution is given together with k linear weight functions, and the goal is to modify the weights by the same deviation vector p so that the input solution becomes optimal…
In a recent paper on the Secretary Problem, Abdolazimi et al. disproved our conjecture on reductions of matroids. The conjecture suggested that any matroid has a reduction to a partition matroid with covering number at most twice that of the original matroid. Though the statement was shown to hold for various matroid classes, it turned…
Our paper titled Rainbow and monochromatic circuits and cuts in binary matroids has been accepted for publication in Discrete Mathematics! We show that if a binary matroid of rank r is colored with exactly r colors, then M either contains a rainbow colored circuit or a monochromatic cut. As the class of binary matroids is…