 
Summary: A Characterization of Seymour Graphs
A. A. Ageev A. V. Kostochka Z. Szigeti y
Abstract
Following Gerards [1] we say that a connected undirected graph G is a Seymour
graph if the maximum number of edge disjoint Tcuts is equal to the cardinality
of a minimum Tjoin for every even subset T of V (G). Several families of graphs
have been shown to be subfamilies of Seymour graphs (Seymour [4][5], Gerards [1],
Szigeti [6]). In this paper we prove a characterization of Seymour graphs which was
conjectured by Seb}o and implies the results mentioned above.
1 Introduction
T. Graphs in this paper are undirected, connected, and may have loops and multiple
edges.
Let G be a graph. For F E(G) and x; y 2 V (G), we write xy 2 F if some edge of
G with endpoints x and y is in F .
For X V (G), the cut Æ(X) is the set of edges connecting X and V (G)nX, N(X) =
fv 2 V (G) n X : v has neighbors in Xg. If X = fxg we write Æ(x), N(x). For F E(G)
and v 2 V (G), let d F (v) denote the degree of v in the subgraph of G spanned by F . A
pair (G; T ) where T is an even subset of V (G) is called a graft.
Let T be an even subset of V (G). If jX \ T j is odd the cut Æ(X) is called a Tcut.
A set F of edges of G is a Tjoin if T = fv 2 V (G) j d F (v) is oddg. Let (G; T ) denote
