Báo cáo toán học: "Ramseyan Properties of Graphs by Ermelinda DeLaVina" doc

... the class of all 4-chromatic graphs. The structure of the red graph is obvious by Corollary, but we do not know which graphs can occur as blue graphs and what are the properties of graphs in which ... Written on the Wall, a list of conjectures of Graffiti. Ramseyan Properties of Graphs by Ermelinda DeLaVina delavina@math.uh.edu Siemion Fajtlowicz siemion@math.uh....

Ngày tải lên: 07/08/2014, 06:20

... of K 3,3 . By Claim 2, G has a minor isomorphic to a graph of the form K 3,3 + e 1 , where e 1 joins two nonadjacent vertices of K 3,3 . If e 2 is any edge of K 3,3 not incident with either of ... colouring of U can be extended to a U-proper (L, 2) ∗ -colouring of G 1 , and that the resulting colouring of X can be extended to an X-pro per (L, 2) ∗ -colouring of G 2 , and t...

Ngày tải lên: 08/08/2014, 01:20

... paths P 2r+1 (with the exception of P 3 ) the only r-terminal graphs? the electronic journal of combinatorics 14 (2007), #R16 6 Structural Properties of Twin-Free Graphs Ir`ene Charon GET - T´el´ecom ... thought of. We give, without proof, one example which gives smaller graphs than the ones in the proof of Theorem 12. In this example, calculations are carried modulo 2r + 1....

Ngày tải lên: 07/08/2014, 15:22

... ϕ(m). Proof. 1. By the multiplicative properties of the Euler function ϕ(t) divides ϕ(n), if t is a divisor of n [13]. Therefore, (9) implies that the nonzero eigenvalues of X n are divisors of ϕ(n). 2. ... 6. In the notation of Lemma 5 the number of common neighbors of distinct vertices a, b in the unitary Cayley graph X n is given by F n (a − b). Proof. Let a, b, z be el...

Ngày tải lên: 07/08/2014, 15:22

... Parvatham, R: Properties of a class of functions with bounded boundary rotation. Ann. Polon. Math. 31, 311–323 (1975) [3]. Noor, KI: On radii of convexity and starlikeness of some classes of analytic ... (http://creativecommons.org/licenses /by/ 2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... show that an interesting family of graphs, namely the family of the complement graphs of U r , denoted by U c r , has a strong orthogonal scheme, with the exception of r ∈{2, 3, 6}.Inotherwords,U c r is ... Oχ(K 5,5 )=5andOχ(K 5,4 )=5. ProofofTheorem1.4: Consider a d-degenerate ordering {v 1 , ,v n } of the vertices of G. We need to create a set {c 1 , ,c k } of k-orthogona...

Ngày tải lên: 07/08/2014, 06:20

... parts are all of size one. Alternately, the complement of such a graph either has no edges or consists of the the disjoint union of three or fewer complete graphs. Proof. The complement of K − 5 is ... similar proofs for complexes of dimension 2 and higher. We conjecture that the answer is “yes,” but the complexity of the proof would be astronomical, even for dimension 2. Hidd...

Ngày tải lên: 07/08/2014, 06:20

... proof of Theorem 28 of [4] can also be adapted to hereditary properties of tour- naments, to produce many properties with different exponential speeds, but we spare the reader the details. Of ... Hereditary properties of combinatorial struc- tures: posets and oriented graphs, to appear in Journal of Graph Theory. [4] J. Balogh, B. Bollob´as and R. Morris, Hereditary propert...

Ngày tải lên: 07/08/2014, 15:23