6 papers
-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 $…
-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 c…
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…
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…
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…
CLM's dependence relation, solitary patterns and -graphs
D. V. V. Narayana, D. Mattiolo, Kalyani Gohokar +1
A connected r-regular graph, where , is an r-graph if each odd cut has at least r edges. Every r-graph is matching covered - a connected graph whose each edge participate…