Edge-connectivity of undirected and directed hypergraphs

140 Index
h(a) the head node of the hyperarc a
t(a) the multiset of tail nodes of the hyperarc a
co(F) {V − X : X ∈ F} (with multiplicity)
χF
F1 + F2
eH(F)
the characteristic set function of the family F
family with characteristic function χF1 + χF2
e∈E maxu∈e |{X ∈ F : u ∈ X, e ⊆ X}|
hX(F) for X ⊆ V and a composition F of X:
Z∈F χZ(v) − χX(v) for
an arbitrary v ∈ V
rM
p
for a matroid M: the rank function of M
∧ (X) max{
p
Z∈F p(Z) : F is a partition of X}
↑ (X) max{
Z∈F p(Z) − hX(F)p(V
p
) : F is a tree-composition of X}
∗ (X) max{
Z∈F p(Z) − hX(F)p(V
p
) : F is a composition of X}
∗ (X, Y ) if p(V ) = 0: max{
Z∈F p(Z) : F is an (X, Y )-composition}
C(p) {x : V → Q : x(Y ) ≥ p(Y ) ∀Y ⊆ V }
B(p) {x : V → Q : x(V ) = p(V ); x(Y ) ≥ p(Y ) ∀Y ⊆ V }