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...

Ngày tải lên: 08/08/2014, 14:23

... 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...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 06:20

... 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...

Ngày tải lên: 07/08/2014, 06:23

... 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...

Ngày tải lên: 07/08/2014, 08:22

... 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...

Ngày tải lên: 07/08/2014, 15:23

... 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...

Ngày tải lên: 07/08/2014, 15:23