Báo cáo toán học: "Discrete Morse inequalities on infinite graphs" docx

... Finally, in Section 4 we give an application of the discrete Morse inequalities which consists on characterizing infinite connected graphs which admit a discrete Morse function with a fixed number ... criticality of the considered function at the infinite. In Section 1, we recall basic Forman’s definitions of discrete Morse function and critical simplex as well as his discrete Mors...

Ngày tải lên: 07/08/2014, 21:21

... ⊆ r · F − is a constant only depending on F and r, this bound holds a.a.s. for all subgraphs J with V (T ) ⊆ V (J) simultaneously. Conditioning on this being the case, we may continue (33) as ... Ramsey games against a one-armed bandit. Combin. Probab. Comput., 12(5-6):515–545, 2003. Spe- cial issue on Ramsey theory. [6] S. Janson. Poisson approximation for large deviations. Random Stru...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 05/08/2014, 15:21

... density conditions on H, one can find an almost perfect matching M in H, i.e., the number of vertices in no edge of M is negligible. In fact, [17] proves something much stronger, namely that one can decompose ... δ<1. Then H contains (1 − 2(t − 1)δ)h vertex disjoint copies of T with the property that V i contains the vertex of each copy corresponding to u i , 1 ≤ i ≤ t. Proof. We use indu...

Ngày tải lên: 07/08/2014, 06:22

... Every infinite connected graph has a vertex of infinite degree or contains a semi -infinite path. Proof. Proposition 8.2.1 in [4].  (i) Infinite trees with no infinite degree vertices Proposition 5. ... an infinite tree with a semi -infinite path or an once-subdivided infinite star has a bijective graceful N/Z + -labeling. Note that an infinite tree contains an one-subdivided infinite...

Ngày tải lên: 07/08/2014, 21:21

... D contains an anti-directed Hamilton cycle. In Section 3 of this paper we turn our attention to (P, Q) vertex-oriented Hamilton cycles. In [1] the following theorem giving a sufficient condition ... G ′ contains a Hamilton cycle. Thus, if δ 0 (D)  3 4 n and |P | is even, then D trivially contains a (P, Q) vertex-oriented Hamilton cycle for any partition V (D) = P ∪ Q of V (D). In Section ... d...

Ngày tải lên: 08/08/2014, 01:20

... conditions stronger than the ones used in standard results for spectral clustering, the results are non-trivial in the sense that mere eigenvalue bounds are not enough to prove them. In Section ... =  log n d . We construct the Quasi-random graph as follows: Construction Starting f rom a single node as ro ot, construct a d(1 +ǫ) degree complete tree T 1 of depth l. Construct another complete...

Ngày tải lên: 08/08/2014, 01:20

... −α)n. As immediate consequences of Theorem 3 we derive the fo llowing sufficient conditions on the expansion parameters ε, b and α which guarantee that all (ε, b, α)-expanders contain every almost ... mentioned result of Alon, Krivelevich and Sudakov [1] that is slightly weaker than Theorem 4. Note that in [1] it is suggested that in the statement o f Theorem 4 the condition on the constant...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 10:20

... 0 for the property that f(t) is an odd function on [α, β]. And the condition that f  (t) is continuous on [α, β] implies that f  (t) is continuous on [α, β], too. Then, by a similar method to ... holds. For convenience, we only consider the special case a = 0. At this moment, the interval [α, β] reduces to [−b, b]. It follows from the construction of f(t), that f (t) is an odd functi...

Ngày tải lên: 20/06/2014, 21:20