... = |U
0
| + 1. Thus all Zelinka graphs have toughness less than
one.
3 Maximal nontraceable graphs with toughness less
than one
Suppose P is a path in a graph G, with endvertices a and z. If we ... of
2-connected non-Zelinka MNT graphs with toughness less than 1.
the electronic journal of combinatorics 15 (2008), #R18 2
Maximal Nontraceable Graphs with
To...
... ✷
Summarizing, we now know all extremal graphs, G with f (G)=2δ +1. The
connected extremal graphs are those given in Theorem 3 along with the trivial ones
with only 2δ + 1 vertices.
We noticed ... the sense that there exist graphs of minimum degree δ with no longer
paths. Our purpose in this article is to characterize all such extremal graphs.
For a graph G with n vertices we...
... and with replacement,
Pr[E(v,j) | C
P
]=1−
1 −
|V
j
|
T (P)
m
(8)
=1− e
−α
j
c/τ
+ O(n
−1
) , (9)
where the passage from (8) to (9) relies on the fact that P has more than one blocks with
Ω(n) ... repeatedly (20 times) removing all vertices of degree less
than 3 from G(n, m = cn). They proved that this pseudograph (i) is uniformly random with
respect to its degree sequence and...
... Tx.Leth(t)=t
2
.Thenh
-1
({0}) = {0},
(H
4
)and(H
5
) are satisfied. Clearly, (2) holds for each x, y Î X with x = y. For each x,
y Î X with x ≼ y and x ≠ y, we have two possible cases.
Case 1. When
x =
1
n
, n ≥ 2 and ... of
maximal point of (X, ≼). Assume that h is a continuous, nondecreasing, and subaddi-
tive function with h
-1
({0}) = {0}, then the relationship defined by (1) is a...