Báo cáo toán học: " For which graphs does every edge belong to exactly two chordless cycles" pps

... the harmonization operation we forget C  and rename C ∗ as C  . For which graphs does every edge belong to exactly two chordless cycles? UriN.Peled 1 and Julin Wu 2 Dept. of Mathematics, Statistics, ... same operation to P  , and so on until we obtain a chordless path P ∗ connecting x 1 to x k .ForacycleC of G andanedgee of C, we can apply the above operation t...

Ngày tải lên: 07/08/2014, 06:20

... graph G(∞, 1) for N (Γ 0 (m)) is of the form v → S( v) → S 2 (v) → S 3 (v) → · ·· → S k−1 (v) → v for an elliptic mapping S ∈ N (Γ 0 (m)) and for some v ∈ ˆ Q . If m  5, then G(∞, 1) does not contain ... section 2, for the definition of suborbital graph.). In this paper, we deal with this conjecture. Before discussing this conjecture we also investigate suborbital graphs for som...

Ngày tải lên: 08/08/2014, 01:20

... study of commuting involution graphs came to the fore in 2003 with the work of Bates, Bundy, Hart (n`ee Perkins) and Rowley, which explored commuting involution graphs for G a symmetric group, or ... vertices x, y ∈ X joined by an edge if and only if xy = yx. Commuting graphs first came to prominence in the groundbreaking paper of Brauer and Fowler [6], famous for containing...

Ngày tải lên: 08/08/2014, 14:23

... tight up to a constant factor. Theorem 3.1 Thereexistsanabsolutepositiveconstanta so that for every n ∆ n ≥ an 2/3 . Thus, ∆ n =Θ(n 2/3 ). Proof. It clearly suffices to prove the lower bound for values ... a unit vector c so that (c t b v ) 2 ≥ 1/θ for every v ∈ V . Therefore, the norm of the projection of each b v on c is at least 1/ √ θ and by assigning appropriate signs to th...

Ngày tải lên: 07/08/2014, 06:20

... forcing Q to have exactly δ + 1 vertices. Hence the final vertex of Q is adjacent to all vertices of Q. Say Q: v = v 1 ,v 2 , ···,v 1+δ .Sincev 1+δ is adjacent to every v i , it follows that every ... condition forces it to be adjacent to every vertex of H. ii) Now suppose f(G)=2δ +1, with δ ≥ 2, and suppose G has a cut vertex v. Note that every path beginning at v lies (ex...

Ngày tải lên: 07/08/2014, 06:20

... Molloy † molloy@cs.toronto.edu Department of Computer Science University of Toronto Toronto, Ontario M5S 3G4, Canada. Abstract We prove that for c ≥ 2.522 a random graph with n vertices and m = cn edges is ... of G.ForC P to hold, every edge of the random graph has to connect vertices from two different blocks. Introducing T (P)=  i<j |V i |·|V j | , (3) the total number of pai...

Ngày tải lên: 07/08/2014, 06:20

... cannotalsobelongtoA. Therefore S ∈Band, similarly, T ∈B. However, S T and S<Tand this is a contradiction. Therefore all red points belong to B. By a similar argument all yellow points belong to B also, ... white points correspond to Young tableau pairs with a shape similar to Figure 3 but with a cell in the (2, 2) position. Unfortunately, not every Young tableau pair of this...

Ngày tải lên: 07/08/2014, 06:22

... vertices exists which is an automorphism of G. Cayley graphs, and in particular, circulant graphs have been studied intensively in the literature. These graphs are easily seen to be vertex transitive. ... vertex number n circulant graphs are known to be the only vertex transitive graphs. Because of their high symmetry, Cayley graphs are ideal models for commu- nication netwo...

Ngày tải lên: 07/08/2014, 06:22

... recognition problem for gc -graphs but also for all graphs generating an association scheme having a connected basic graph (X, γ i )ofdegree ≤ 2 and for graphs having a factor graph which is a cycle. ... such knowledge, too. For this reason it seems reasonable to look more closely to the structure of general cyclotomic circulants and try to find a polynomial time recogniti...

Ngày tải lên: 07/08/2014, 06:22

... for every H ∈B(m, ∆). In [1] and [2] the problem of finding minimum M = M(m) for which there exists an (m, ∆)-universal graph with M edges is investigated. Here we apply Theorems 1.3 and 1.4 to ... tower type for Szemer´edi’s uniformity lemma, GAFA, Geom. Funct. Anal. 7 (1997), 322-337. [5] R. L. Graham, V. R¨odl and A. Ruci´nski, On bipartite graphs with linear Ramsey numbers, C...

Ngày tải lên: 07/08/2014, 06:23