Báo cáo toán học: "Lower Bounds for the Average Genus of a CF-graph" doc

... such a polygon do not change genus of such a surface. Operation 1: Aaa − ∼ A, Operation 2: AabBab ∼ AcBc, Operation 3: AB ∼ {(Aa), (a − B)}, A A a a A B a b b a A B c c A B A Bc c Figure 4: Operation ... attaching ears serially or by bar -amalgamation of a cactus to G N The authors of [5] discussed a Kuratowski type theorem for average genus of graph...

Ngày tải lên: 08/08/2014, 12:23

... is, that for larger values of k the “irregular” solutions of the linear inequalities no longer yield a negligible amount in the necessary estimations. The aim of this paper is to present a first ... 2006; Accepted: Mar 15, 2007; Published: Mar 28, 2007 Mathematics Subject Classifications: 94B65 Abstract Let k 3 (n) denote the minimal cardinality of a ternary code of...

Ngày tải lên: 07/08/2014, 15:22

... proof. Given the informal discussion above, the proof of Theorem 1.1 looks very roughly as follows. At the first part of the proof we consider the graph G(n, ρ) for a relatively large ρ, and show that for ... edge that appears in T appears exactly once † . The advantage of T being good is that for many of the edges that appear in T , the events that these edges...

Ngày tải lên: 07/08/2014, 21:21

... before, the evaluation of the Tutte polynomial at these points is #P-hard for planar bipartite graphs [11] and even for grid graphs of maximum degree 3 [12]. The approach for obtaining the bounds ... Also, if H is a subgraph of G and G has no loops, then the number of acyclic orientations of G is at least that of H;thisisbecauseevery acyclic orientation of H...

Ngày tải lên: 07/08/2014, 07:21

... subset of V (G)thenU denotes the subgraph of G induced by U. AgraphG is hamiltonian if it has a hamiltonian cycle (a cycle containing all the vertices of G), and traceable if it has a hamiltonian ... AgraphG is maximal nontraceable (MNT) if G is not traceable, but G + e is traceable for each e ∈ E( G). ∗ This material is based upon research for a thesis at the Univers...

Ngày tải lên: 07/08/2014, 13:21

... minimal cardinality of a q-ary code of length n and covering radius R. Recently the authors gave a new proof of a classical lower bound of Rodemich on K q (n, n − 2) by the use of partition matrices ... of checking every possible partition, but adapted to manual computations. It can be applied with a reasonable amount of work when k = 3 and n and q are not too big (s...

Ngày tải lên: 08/08/2014, 01:20

... hexagonal lattices as well as the square lattice with diagonals (king grid). For each of these graphs, there is a characterization so that the ver tex set is Z × Z. Let Q m denote the set of ... 2-identifying code of the square grid is at least 3/19 ≈ 0.1579. Theorem 2 can be improved via Lemma 9, which has a more detailed and technical proof than the prior lemmas. The...

Ngày tải lên: 08/08/2014, 12:22

... B i (A i ,B i ∈F). Otherwise say the union is bad. Suppose first A ∪ B is bad for at most a fraction 1 n of the ordered pairs (A, B) (A, B ∈ F ). Consider the random variable X = A B. It has entropy at least (1 ... defined as the maximum value of α (as a function of p) which allows equations (3), (4) and (5) to be satisfied. Further calculations show ψ(p) is increasing...

Ngày tải lên: 07/08/2014, 06:22

... applications, Handb ook of algebra, North-Holland, Am- sterdam, 3, (2003), 907–959. [8] A. Molev, Yangians and classical Lie al gebras, Mathematical Surveys and Mono- graphs, American Mathematical Society, ... that these matrices are inverses of each other. Therefore, each minor of H − is equal to the complementary cofactor of the transpose of E, which implies the equality o...

Ngày tải lên: 08/08/2014, 01:20

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Ngày tải lên: 05/08/2014, 15:21