Báo cáo toán học: " On cubic planar hypohamiltonian and hypotraceable graph" pptx
Báo cáo toán học: " On cubic planar hypohamiltonian and hypotraceable graph" pptx
... electronic journal of combinatorics 18 (2011), #P85 6
2 Cubic planar hypohamiltonian graphs on 70 and
88 vertices
In this section we present our cubic planar hypohamiltonian graphs on 70 and 88 ... 0-
and 1-faces together non-2-faces.
Claim 2.1. A cubic planar hypohamiltonian graph has at least three non-2-faces.
Proof. Let D be an arbitrary cubic planar hypoh...
Báo cáo toán học: " On externally complete subsets and common fixed points in partially ordered sets" potx
... in
Abu-Sbeih and Khamsi Fixed Point Theory and Applications 2011, 2011:97
http://www.fixedpointtheoryandapplications.com/content/2011/1/97
Page 5 of 8
Proof.Let
M ∈ EC
(
X
)
.Then,M is convex and Dedekind ... Abu-Sbeih and Khamsi: On externally complete subsets and common fixed points in partially
ordered sets. Fixed Point Theory and Applications 2011 2011:97.
Abu-Sbeih and Kh...
Báo cáo toán học: "On a Class of Constant Weight Codes" pptx
... implied constants depend only on n.ThinkingatC(q, 2) only,
we see that in fact we managed to construct an explicit example of (q
2
−q)/2such
‘almost-independent’ random subsets of F
q
, each one having ... codewords.
Also, by using results on Artin L−series, it is shown that the distribution of the 0’s
and 1’s in the codewords we constructed is quasi-random. Our construction uses
charac...
Báo cáo toán học: "On a conjecture concerning dyadic oriented matroids" pptx
... electronic journal of combinatorics 6 (1999), #R23 5
matroid, we apply Proposition 1 and conclude that A
k
and A
k
are equivalent repre-
sentations of M
k
. Each representation is in standard ... necessary condition on the ratio of agreement to disagreement in sign of its signed
circuits and cocircuits. It is the point of this note to show that this necessary condition
is not sufficie...
Báo cáo toán học: "On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices" pps
... construction of section 3 we rely on the following definition and theorem.
Definition 5.4 Let G be a graph and let G
be an even subdivision of G.LetD
be an
orientation of G
. An orientation D of G induced ... e belongs to
[x
i
1
,x
i
2
] and the other one belongs to [x
i
3
,x
i
4
]. Similarly, if e ∈ E
i
2
then e is embedded
entirely on B
i
2
and one end vertex of e belongs to...
Báo cáo toán học: " On a Partition Function of Richard Stanley" pptx
... denote the numerator on the right-hand side of
(3) and τ
2N+1
(q, z,y) denote the numerator on the right-hand side of (4). If we can show
that τ
N
(q, z,y) satisfies (14) and (15), then noting ... proved
similarly.
4 Conclusion
As is obvious, Theorem 1 is easily proved once it is stated, but the sums appearing in (3)
and (4) seem to arise from nowhere.
I note that by considering the...
Báo cáo toán học: "On self-complementary cyclic packing of forests" pptx
... v
is the only neighbour of l. Let w be the second neighbour of v. In this subcase let
F
= F − V (T) − {l, v}. We put the vertices of T on f
3
and f
4
and the vertices l and v
on f
1
and f
2
, ... it on f
3
and then put the vertex u on the
place just left by x.
4 Generalizations
Theorem 6 Let p and q be integers such that p ≥ 1, q ≥ 0 and let F be a forest of order
at m...
Báo cáo toán học: "On small dense sets in Galois planes" pptx
... F
∗
p
, and then the size of D is 2
q
p
+p. A
dense set of the same size and contained in three non-concurrent lines was constructed in
[6, Thm. 3]. It can be proved by straightforward computation ... are now in a position to prove the main result of the section.
Proposition 2.5. Let F
m
(X, Y ) be as in (4). The equation F
m
(X, Y ) = 0 has more than
q solutions if and only if either m...
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