Báo cáo toán học: "Bartholdi Zeta Functions of Fractal Graphs" pptx

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Ngày tải lên: 05/08/2014, 15:20

... Denley’s Theorem 4. References 1. Denley, T., The Independence number of graphs with large odd girth, The Electronic Journal of Combinatorics 1 (1994) #R9. 2 We can now prove the following theorem. Theorem ... is sharp for the regular complete bipartite graphs K aa . The above results are readily extended to graphs of larger odd girth. Lemma 2: Let G have odd girth...

Ngày tải lên: 07/08/2014, 06:20

... chordless. The length |C| of a cycle C is the number of its edges. The length (B) of a cycle basis B is sum of the lengths of its cycles: (B)=  C∈B |C|.Aminimal cycle basis is a cycle basis with minimal ... . 5. Minimal Cycle Bases of Outerplanar Graphs Let (G, V ) be a 2-connected outerplanar graph. The set T = H \{(1,n)} is a spanning tree of G(V,E). The fun...

Ngày tải lên: 07/08/2014, 06:22

... tight. The odd edge-connectivity of a graph G is the size of a smallest odd edge cut of G.The odd girth of G is the length of a shortest odd cycle of G. Zhang [19] proposed a strengthing of Jaeger’s ... of length at least 2k. For otherwise, for any internal vertex x of a thread of length the electronic journal of combinatorics 8 (2001), #R25 3 Circular chromati...

Ngày tải lên: 07/08/2014, 06:22

... monotone subsequences of length 3 in L, R are also such subsequences of S.There are no monotone subsequences of S containing both 0 and n − 1. There are no monotone subsequences of S of the form a, ... up of k monotone descending subsequences, each of length n/k or n/k; clearly it has no monotone ascending subsequences of length k +1, and any monotone descendin...

Ngày tải lên: 07/08/2014, 07:21

... Theorem 10 makes it clear that the problem of factoring the generalized zeta function is really a problem of factoring the zeta function of a bipartite graph. Fortunately, in [11], Hashimoto deals with this ... instead. 3.1. Consequences of the Factorization Our first observation is that the zeta function of a hypergraph is a non-trivial gener- alization of the...

Ngày tải lên: 07/08/2014, 13:21

... runs over all equivalence classes of prime, reduced cycles of G, and | C | is the length of C. Zeta functions of graphs started from zeta functions of regular graphs by Ihara [8]. In [8], he showed ... Sato [10] showed that the zeta function of a regular covering of G is a product of L -functions of G. Stark and Terras [16] treated zeta functions of bipartit...

Ngày tải lên: 07/08/2014, 13:21

... give a decomposition formula (Theorem 4) for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of some ... By the fact that B H = B H ∗ . ✷ 3 Bartholdi zeta functions of (d, r)-regular hypergraphs At first, we state a decomposition formula for the Bartholdi zeta function of a semiregular...

Ngày tải lên: 07/08/2014, 13:21

... referee for the useful remarks. the electronic journal of combinatorics 14 (2007), #N21 6 Regular spanning subgraphs of bipartite graphs of high minimum degree B´ela Csaba ∗† Submitted: Aug 1, 2007; ... electronic journal of combinatorics 14 (2007), #N21 2 3.2 Proof of part II For proving part II of the theorem we want to construct a class of balanced bipartite...

Ngày tải lên: 07/08/2014, 15:22

... a perfectly balanced partition almost surely. Smoothed Graphs. Smoothed analysis studies the behavior of objects after adding a small amount of randomness. This concept was introduced in the context of ... journal of combinatorics 16 (2009), #N14 6 • ∆(G) − δ(G) ≤ 2αn. • G has a degree matching of size at least 2αn. In the course of the proof of Lemma 5, we need the follo...

Ngày tải lên: 07/08/2014, 21:21

... proof of Theorem 1, and discussed three different zeta functions of any graph. Various proofs of Bass’ theorem were known. Kotani and Sunada [15] proved Bass’ theorem by using the property of ... Ihara zeta function of a fractal graph, and gave a determinant expression of it. We define the Bartholdi zeta function of a fractal graph, and present its determinant expressi...

Ngày tải lên: 07/08/2014, 21:21

... maximized when G = K n . Some improvements of (1) for 1/ ( n − 2) < λ < 3, λ = 1 are given in Sections 4 and 5. 3 Maximal flat antichains of minimum si ze In this section we show that the ... inequality implies  x∈V d(x) 2 ≥ 4|E| 2 n , the electronic journal of combinatorics 16 (2009), #R69 17 Maximal at antichains of minimum weight Martin Grăuttmăuller Hochschule...

Ngày tải lên: 07/08/2014, 21:21

... distinguishing chromatic number of K n,n − M We denote by K n,n − M the graph obtained from the complete bipartite graph K n,n by deleting the edges of a perfect matching. This graph arises in the proof of ... c(b k−1 ) = ∆. Let S ⊆ V (G) consist of the union of all the vertices in levels 0 through k − 1 of T . Because of our choice of C and r, G[S] ∼ = T [S], with a ll le...

Ngày tải lên: 07/08/2014, 21:21

... graphs with maximum Laplacian spread among all tricyclic gr aphs of order n ≥ 11. Moreover, fo r 5 ≤ n ≤ 10, if G is one with maximum Laplacian spread of all tricyclic gra phs of order n, then G ... vertices of the star, respectively [4]. A tricyclic graph is a connected graph in which the number of edges equals the number of vertices plus two. In this paper, we stud...

Ngày tải lên: 07/08/2014, 21:21

... exp(− ¯ d min /(2C)), the electronic journal of combinatorics 16 (2009), #R138 44 The spectral gap of random graphs with given expected degrees ∗ Amin Coja-Oghlan University of Edinburgh, School of Informatics Crichton ... graphs with with given degree sequences. Random Structures and Algorithms 32 (2008) 1–19 [7] Chung, F., Lu, L.: Connected components in rand...

Ngày tải lên: 08/08/2014, 01:20