A cut C:=∂(X) of a matching covered graph G is a separating cut if both its C-contractions
G/X and G/X are also matching covered. A brick is solid if it is free of nontrivial separating …

A bi‐subdivision of a graph J is a graph H obtained from J by subdividing each of its edges
by inserting an even number of vertices. A matching covered subgraph H of a matching …

The bicontraction of a vertex v of degree two in a graph, with precisely two neighbours v1
and v2, consists of shrinking the set 1v1, v, v2l to a single vertex. The retract of a matching …

The bicontraction of a vertex $ v $ of degree two in a graph, with precisely two neighbours $
v_1 $ and $ v_2 $, consists of shrinking the set $\{v_1, v, v_2\} $ to a single vertex. The …

A brick is a 3‐connected graph such that the graph obtained from it by deleting any two
distinct vertices has a perfect matching. A brick G is near‐bipartite if it has a pair of edges α …

A nontrivial connected graph is matching covered if each of its edges lies in a perfect
matching. Two types of decompositions of matching covered graphs, namely ear …

In this paper we show that, with 11 exceptions, any matching covered bipartite graph on n
vertices, with minimum degree greater than two, has at least 2n-4 perfect matchings. Using …

McCuaig proved a generation theorem for braces, and used it as the principal induction tool
to obtain a structural characterization of Pfaffian braces. A brace is minimal if deleting any …

A 3-connected graph is a brick if the graph obtained from it by deleting any two distinct
vertices has a perfect matching. The importance of bricks stems from the fact that they are …

McCuaig [12] provou um teorema de geração para braces e o usou como uma ferramenta
de indução para obter uma caracterização estrutural de braces Pfaffianos [13]. Um brace é …