... probability that a random threshold graph is Hamiltonian. There is
a nice connection between Hamiltonicity and a threshold graph’s creation sequence. For more
background on Hamiltonian threshold graphs, ... natural, equivalent models for random threshold graphs and use
these models to deduce a variety of properties of random threshold graphs. Specifically, a
random threshold graph...
... subgraph of a threshold graph is
again a threshold graph, so G − u is threshold.
Conversely, suppose u is an extremal vertex of G and that G − u is a threshold graph. Let x
be a threshold representation ... property of being a threshold graph is a hereditary property of
graphs. By this we mean
• if G is a threshold graph and H is isomorphic to G, then H is a threshold graph, a...
... 4,
both graphs coincide with P
4
.
Let Γ
0
=
{H ∪ K
2
|H is a connected threshold graph} ∪
{H ∨ O
2
|H is a disconnected threshold g r aph} ∪
{NT
1
(2n)|n ∈ IN} ∪ {NT
2
(2n)|n ∈ IN}.
For each ... Pati, Laplacian spectrum of weakly quasi -threshold graphs,
Graphs and Combinatorics, to appear.
[2] H. Christianson and V. Reiner, The critical group of a threshold graph, Linear and
its Appl...
... Random-Cluster Model, Springer, Berlin, 2 006.
[13] G. R. Grimmett and B. T. Graham, In fluence and sharp threshold theorems f or
monotonic measures, Annals of Probability 34 (2006), 172 6–1745.
[14] G.
... random intersection graphs, threshold functions,
connectivity, Hamilton cycle, perfect matching, coupling
Abstract
We present a new method which enables us to find threshold functions for many
properties ... enough to give some partial results on the threshold functions
for other properties of G (n, m, p). However we present here graph properties for which the
threshold functions obtai...