Báo cáo toán học: "The cover pebbling theorem Jonas Sj¨strand o" docx

... that admits no cover pebbling, all pebbles may be concentrated to one of the fat nodes 1 with cover pebbling still not possible. Proof. Start with a distribution that admits no cover pebbling. If ... cover pebbling from f exceeds the total value of the pebbles. Therefore, cover pebbling is not possible with all pebbles initially on f .  4 The cover number for some classe...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 05/08/2014, 10:20

... 4-Color Theorem and since we do not want to use this powerful theorem for our application if not necessary, we state a weaker result with an elementary proof: Lemma 2.3 Let G be as in Theorem ... 2.5. Otherwise, χ(H(G)) = χ(G) ≤ 3 by Theorem 1.1. 3 List-coloring planar and projective planar graphs The main results of this section are Corollary 3.4 and Theorem 3.8 which extend Theore...

Ngày tải lên: 07/08/2014, 06:20

... we give combinatorial proofs of the q-binomial theorem and Theorems 1.2 and 1.3. Our combinatorial proof of the q-binomial theorem is based on Theorem 2.1, and is essentially the same as that ... journal of combinatorics 10 (2003), #R34 2 2 A Theorem on Partitions The following theorem is crucial to prove Theorems 1.1–1.3 combinatorially. Theorem 2.1 Given m ≥ 1, the number of par...

Ngày tải lên: 07/08/2014, 07:21

... c d+1 = 0). 5 The spectral excess theorem We are ready now for the spectral excess theorem. We shall state and prove it in a bit stronger form than earlier stated. Theorem 1. Let Γ be a connected ... antipodal distance-regular graphs. The usefulness of the spectral excess theorem is for example demonstrated in the re- cent discovery of a new family of distance-regular graphs with the s...

Ngày tải lên: 07/08/2014, 21:20

... − 1. Plugging this into Theorem 3.8 yields the claim. Theorem 3.15. For d-dimensional torus graphs (d  1 constant),  EC(G) = O(n 1+1/d ). Proof. Also here, we apply Theorem 3.5 and use the ... sequence can only slow down the covering pro ces s. Hence it suffices to bound  EC  (G) with Theorem 3.8. We will now upper bound all three summands involved in Theorem 3.8. By two classic r...

Ngày tải lên: 08/08/2014, 12:23

... sequence of pebbling moves. The t -pebbling number of (G, ω) is defined as π t (G, ω) = max{π t (G, ω, x) : x ∈ V (G)} and we write π t (G) for the unweighted case with ω ≡ 2. Graph pebbling originated ... to ω(v) = 2 for all v ∈ V (G).) More formally, if e = {u, v} ∈ E and p is a pebbling distribution such that p(u) ≥ ω(e), then a pebbling move allows us to replace p with the distriu...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 10:20

... Kites contained vertex Figure 21: Two kites in the light region Singer’s Theorem [Sin71] follows from the previous lemmas. A stronger version of the theorem is given next. Theorem 4.7 An optimal rectilinear drawing of ... > 61. Theorem 4.15 ν(K 10 ) > 61. Proof: By way of contradiction assume that ν(K 10 ) = 61. By Theorem 4.14 the inner hull must be a convex quadrilateral. Re...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 07/08/2014, 13:21