Báo cáo toán học: "he map asymptotics constant tg" ppsx

... (4) where u g ∼ K . = 0.1034 is a constant. 2 Cubic Maps A map is called cubic if all its vertices have degree 3. The dual of cubic maps are called triangular maps whose faces all have degree ... families. Richmond and Wormald [5] showed that many families of unrooted maps have asymptotics that differ from the rooted asymptotics by a factor of four times the number of edges. See Goulde...

Ngày tải lên: 07/08/2014, 15:23

... k th coronas β : C k (Q) →C k (Q  ) restricts faithfully to a local mapping α Q between the face lattices of Q and Q  , and all these local mappings fit together coherently to determine an extension of ... complexes α : C k (P ) →C k (P  )withα(P )=P  ;suchamapα is called an isomorphism of centered k th coronas. In this situation, since α maps P to P  ,italso preserves distances from the...

Ngày tải lên: 07/08/2014, 08:22

... [10] under the name of star coloring. For r > 0, an r-circular edge-coloring of a graph G is a mapping c : E(G) → [0, r) such that 1 ≤ |c(e) − c(f)| ≤ r − 1 for every two adjacent edges e and ... the conjecture of Jaeger and Swart [3] that the girth of every snark is bounded by an absolute constant by constructing snarks of arbitrarily high girth. However, the conjecture holds in an appr...

Ngày tải lên: 07/08/2014, 13:21

... Lemma 4.2 and the definition of the map A we have d ∗ i = d ∗ j and e ∗ i = e ∗ j whenever i, j ∈ B  , for some . We now have, using the definition of the map A, c 1 d ∗ 1 + c 2 d ∗ 2 + ···+

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 07/08/2014, 13:21

... than X. Now give o pposite labels to the corners in the circuit in X and subtract and add another constant k ′′ in a similar way to obtain another matrix X ′′ in P (n) with at least one more non–inner ... conv{(z ω(1) , z ω(2) , . . . , z ω(n) ) | ω ∈ S n }. (9) Also, for such a vector z, let φ z be the mapping from the set of n × n real matrices to R n defined by φ z (X) = zX, for any n × n...

Ngày tải lên: 07/08/2014, 21:21

... for any constant C > 0 there exists a constant K > 0 such that P  |X x,y − E(X x,y )| > K ¯ d −1/2 min   C −n . Combining Lemmas 5.2 and 5.3, we conclude that there is a constant ... remaining task is to estimate the contribution of the pairs (i, j) ∈ Q 2 . Lemma 5.8 There is a constant c 8 > 0 such that  (i,j)∈Q 2  (u,v)∈A i ×B j , u=v m ′ uv x u y v  c 8 ¯ d −1/2...

Ngày tải lên: 08/08/2014, 01:20

... 1|G ′ )  (1 − p ij ) r  (1 − p ∗ ) r  e −p ∗ r . (31) Here p ∗ r  c ′ n 7/3 (ln n) −2 , and the constant c ′ depends on β, M, and q ′ . Next, we apply Markov’s inequality to the conditional probability P(N ... [2] for m = ⌊n α ⌋, α = 1, and by Lager˚as and Lindholm [14] for m = ⌊βn⌋, where β > 0 is a constant. They have shown, in particular, that, for α  1, the largest connected c...

Ngày tải lên: 08/08/2014, 12:22

... chromatic number for maps. Problem: Classify all maps M with χ D (M) = χ(M) + 3. Problem: Classify all planar maps M with χ D (M) = χ(M) + 2. Problem: For small genus g, classify all maps M wi th χ D (M) ... the planar map is a triangulation [20]. We observe that the argument of Theorem 5.2 can be applied to maps in higher genus surfaces: Theorem 5.3 T here are only finitely many 3-connected...

Ngày tải lên: 08/08/2014, 12:23

Ngày tải lên: 08/08/2014, 14:22