5 citations · 17 across the 14 of their papers we have counts for
14 papers
Cubic graphs, -minors and conformal minors
Nishad Kothari, Orlando Lee, Cláudio L. Lucchesi +1
It is well-known that any class of simple graphs, that is characterized by finitely many forbidden minors, also admits a characterization by finitely many forbidden topological min…
-matchability in cubic graphs
Santhosh Raghul, Nishad Kothari
A vertex of a 2-connected cubic graph is -matchable if has a spanning subgraph in which has degree three whereas every other vertex has degree one, and we let $λ…
Solitude patterns of -graphs via CLM's dependence relation
D. V. V. Narayana, D. Mattiolo, Kalyani Gohokar +1
Recently, Goedgebeur, Mazzuoccolo, Renders, Wolf and the second author [Cubic graphs with edges in exactly one perfect matching, J. Graph Theory 112 (2026), 276-289] proved that ev…
-free matching covered graphs: characterization and consequences
Rohinee Joshi, Santhosh Raghul, Ajit A. Diwan +1
The Ear Decomposition Theorem of Lovász & Plummer (1986) implies that every matching covered graph (MCG), except and cycles, contains (at least) one of and as a con…
Planar cycle-extendable graphs
Aditya Y Dalwadi, Kapil R Shenvi Pause, Ajit A Diwan +1
For most problems pertaining to perfect matchings, one may restrict attention to matching covered graphs - that is, connected nontrivial graphs with the property that each edge bel…
Extremal minimal bipartite matching covered graphs
Amit Kumar Mallik, Ajit A. Diwan, Nishad Kothari
A connected graph, on four or more vertices, is matching covered (aka 1-extendable) if every edge is present in some perfect matching. An ear decomposition theorem exists for bipar…
Minimal Braces
Phelipe A. Fabres, Nishad Kothari, Marcelo H. de Carvalho
McCuaig (2001, Brace Generation, J. Graph Theory 38: 124-169) proved a generation theorem for braces, and used it as the principal induction tool to obtain a structural characteriz…
Equivalence classes in matching covered graphs
Fuliang Lu, Nishad Kothari, Xing Feng +1
A connected graph , of order two or more, is matching covered if each edge lies in some \pema. The tight cut decomposition of a matching covered graph yields a list of brick…
Birkhoff-von Neumann Graphs that are PM-compact
Marcelo H. de Carvalho, Nishad Kothari, Xiumei Wang +1
A well-studied geometric object in combinatorial optimization is the perfect matching polytope of a graph . In any investigation concerning the perfect matching polytope, one ma…
On essentially 4-edge-connected cubic bricks
Nishad Kothari, Marcelo H. de Carvalho, Cláudio L. Lucchesi +1
Lovász (1987) proved that every matching covered graph may be uniquely decomposed into a list of bricks (nonbipartite) and braces (bipartite); we let denote the number o…
On Two Unsolved Problems Concerning Matching Covered Graphs
Cláudio L. Lucchesi, Marcelo H. de Carvalho, Nishad Kothari +1
A cut of a matching covered graph is a separating cut if both its -contractions and are also matching covered. A brick is solid if it…
Generating simple near-bipartite bricks
Nishad Kothari, Marcelo H. de Carvalho
A brick is a -connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. A brick is near-bipartite if it has a pair o…
Generating Near-Bipartite Bricks
Nishad Kothari
A -connected graph is a brick if, for any two vertices and , the graph has a perfect matching. Deleting an edge from a brick results in a graph wi…
Approximation Algorithms for Digraph Width Parameters
Shiva Kintali, Nishad Kothari, Akash Kumar
Several problems that are NP-hard on general graphs are efficiently solvable on graphs with bounded treewidth. Efforts have been made to generalize treewidth and the related notion…