Báo cáo toán học: "Long path lemma concerning connectivity and independence number" pdf

... other standard notation comes from [1]. the electronic journal of combinatorics 18 (2011), #P149 2 Long path lemma concerning connectivity and independence number Shinya Fujita ∗ Alexander Halperin † Colton ... theorem and, following the proofs presented in [4], we prove the following lemma which is o ur main result. Lemma 1 Let k ≥ 1 be an integer and let G be a g raph of...

Ngày tải lên: 08/08/2014, 14:23

... escalating Dyck path, and the action of the first-return and the sink-or-float bijections. 643125 12 789643125 312467958 a) b) 2 Dyck paths and classical permutation avoidance A panoramic Dyck path of ... a 1 <a 2 and a 3 <a 4 (note that s 3 and s 4 belong to the same horizontal edge); since there are at least two long horizontal edges and s 2 and s 3 belong respectively...

Ngày tải lên: 07/08/2014, 07:21

... (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 form with respect to the same base, so ... follows: (D k ) ij =                1, if j =1; 1, if i = j − 1andj≥2; 2, if j = 2 and i ≥ 2; 2, if i = j =2k+2; −1, if i ≥ j and 3 ≤ j ≤ 2k +1; 0, otherwise. Let e 1 ,e 2 ,...

Ngày tải lên: 07/08/2014, 06:20

... = s,andifx = l − s +3 and x  = s +1, then x − s +2=l − s +3− s − 2=l − 2s +5=s +1. So,if4≤ x  ≤ x − s +2,thenx  ≤ s and hence x  +(x − s) − 1 ≤ x − 1, and so P  is a heterochromatic path ... 10l +7 ifs ≤ 2l − k − 1andk ≡ 1, 4(mod 5); 6k − 10l +10 if s ≤ 2l − k − 2andk ≡ 2(mod 5); 2ifs =2l − k and k ≡ 1, 4(mod 5); 1ifs =2l − k or s =2l − k − 1andk ≡ 2(mod 5), ≥ 1 and x  − (x...

Ngày tải lên: 07/08/2014, 13:21

... <v(G)andv(Y ) <v(G). Now  2G F  =  2H F  follows from the fact that G and H have identical vertex decks and Kelly’s Lemma. The following corollary is an immediate consequence of the above lemma. Corollary ... to G. 1. When F 2 =2G, then Equation (10) follows from Lemma 2.9 and Corollary 2.10. 2. When F 1 = G + X and F 2 = G + Y ,andv(X) <v(G)andv(Y ) <v(G), we ha...

Ngày tải lên: 07/08/2014, 13:21

... he path is called a short overpath and in the second, a long overpath. Note that both long and short overpaths may use monobridges. (In Figure 4.1, P 1,3 denotes a short {x 1 , x 3 } overpath and ... overpath gives rise to both a short {x i , x i+2 } overpath and a short {x i+1 , x i+3 } overpath via a suitable selection of an edge joining x i+1 and N ′ i+1 and an edge joining x...

Ngày tải lên: 08/08/2014, 12:23

... 21-34. [3] I.M. Gessel and X. Viennot, “Binomial determinants, paths, and hook length formu- lae”, Adv. Math 58 (1985), 300-321. [4] I.M. Gessel and X. Viennot, “Determinants, paths, and plane partitions”, ... subscripts i and j of h i (x) and h j (y) determine the number of horizontal steps east and west, respectively, o f the corresponding lattice paths. The north-east paths P...

Ngày tải lên: 08/08/2014, 12:23

... is thought to be active, while the other three are silenced. In A6, both iab-5 and iab-6 are active, and iab-7 and iab-8 are silenced, but only iab-6 drives the expression of Abd-B. Similarly, ... avoid other pro- moters, and to locate and physically approach their proper target promoter in the viscous environment of the nucleus. Somatic pairing of chromosomes and the regulation o...

Ngày tải lên: 20/02/2014, 01:20

... of macrocells and femtocells. 2- Self-optimization and auto-configuration: The femtocell is expected to operate in a plug and play fashion to ease installation, conf igurat ion, and man- agement. ... Gaussian independent and identically distributed (i.i.d.) random variables with zero mean and variance s 2 . In channel sensing, we are interested in the probability of detection, P d...

Ngày tải lên: 20/06/2014, 20:20

... values of D RSU would lead to longer multi-hop paths, in terms of number of traversed nodes, and therefore lower effective bandwidths. Only for R = 150 m and in the motorway scenario (this behavior ... forwarding within an area, and affected protocol layers. Figure 3: Geographical area partitioning and IPv6 virtual link abstraction. Figure 4: Multi-hop connectivity between a car and...

Ngày tải lên: 20/06/2014, 20:20