... resulting in ten obstructions to clustered pla-
narity [6].
the electronic journal of combinatorics 18 (2011), #P159 5
A Note on Obstructions to Clustered Planarity
Jamie Sneddon
Department of ... Obstructions to Clustered Planarity
We use Theorem 1 to find the obstructions to clustered planarity. Note that all ss-planar
digraphs are also clustered planar. We...
... Natural
Science Foundation of China (11061012), the project supported by program to Sponsor Teams for Innovation in the
Construction of Talent Highlands in Guangxi Institutions of Higher Learning ... becomes. By this argument, one should
also expect to get stronger results if we use larger weights. And it would be of considerable interest to determine the
optimal weights.
On the other...
... a maximal nonhamiltonian split gr aph.
Since H
4,6
is nonhamiltonian, by Theorem 4 the graph H
4,6
[X, v
∗
1
]isnon-
hamiltonian. Therefore, if T has a Hamilton cycle C then C must contain the
edge ... both to the first question for all k ≥ 4
and to the second question for all k ≥ 5.
We would like to note that there is an interesting discussion about the
Burkard–Hammer condition in [9]...
... <k<7/4+. Note that 7/4isthethreshold of repetition
1
Thanks to Kirby Baker for the use of his software which allowed the author to make these discoveries
concerning abcacb.
A note on antichains ... to avoid than finite
antichains! That is, to avoid a finite antichain over S it may be necessary to move to a larger
alphabet, whereas this is not the case with infinite antic...
... 05E05.
Notation
Let P (n) denote the number of (unordered) partitions of n into positive integers,
and let φ denote the Euler totient function. Let V be the standard n-dimensional
representation of ... n ≤ 23. Note that D(n) appears to
be close to E(n + 1). We don’t have any theoretical explanation of this observation.
the electronic journal of combinatorics 7 (2000), #R6 8
Proposition...
... for a constant κ<2/3, then it outputs a cover graph whp. Note
that the output graph will have whp girth equal to 4. On a related note we point to
[8] which surveys constructions of non cover ... Combinatorica 11 (1991)
45-54.
the electronic journal of combinatorics 7 (2000), #R19 9
[8] O. Pretzel, Orientations and Edge Functions on Graphs, in: A.D.Keedwell
(ed.), Surveys in Com...
... information on Maple) implementation of the downhill simplex function optimization
method (see [13] for a good description of the method and a C implementation) to the
maximize the expression. This ... now consider an arbitrary term of the double sum that appears in (7) and
examine for which values of r it converges to 0. If we find a condition on r that forces
such a term to converg...