Báo cáo toán học: "Pan-factorial Property in Regular Graphs" pot

... and M. D. Plummer, Matching Theory, Akad´emiai Kiad´o, Budapest, 1986 [6] H. Minc, Nonnegative Matrices, Wiley, 1988 [7] V. Răodl and A. Rucinski, Perfect matchings in -regular graphs and the ... bound follows by applying the Stirling approximation formula for factorials. It is worth noting that since every -regular graph with density d and 2n vertices contains, in each color cla...

Ngày tải lên: 07/08/2014, 06:22

... k-connected, k-ordered, and balanced bipartite graph. The minimum degree is δ(G)=d(v)=|A 1 | for any vertex v ∈ B 2 ∪ A 2 ,thusthe minimum degree condition is just missed. But G is not k-ordered ... the following: Corollary 12. Let k ≥ 3 and let G be a k-ordered balanced bipartite graph of order 2n. If δ(G) ≥ n 2 + k−1 4 , then G is k-ordered hamiltonian. the electronic journal of...

Ngày tải lên: 07/08/2014, 07:21

... short cycles in random regular graphs, J. Combin. Theory, Ser. B 31 (1981) 168–182. [11] N. C. Wormald, Models of random regular graphs. In J.D. Lamb and D.A. Preece (eds.), Surveys in Combinatorics ... questions, the most “interesting” subgraphs are the cycles. For this reason we consider only cycles in this paper. The girth of the graph is an interesting property which...

Ngày tải lên: 07/08/2014, 08:20

... 1-factor F containing e  and thus F is the 1-factor avoiding e. the electronic journal of combina torics 12 (2005), #N23 2 Pan-factorial Property in Regular Graphs ∗ M. Kano 1 and Qinglin Yu 23 1 Department ... 1-factor containing e,so does G ∗ . By Theorem 1, G ∗ has a k-factor containing e and another k-factor avoiding e for all k,1≤ k ≤ 2r − 1. Deleting the matching M from G ∗ ,weo...

Ngày tải lên: 07/08/2014, 08:22

... classifying one-factorizations of regular graphs are studied. The smallest open case is currently graphs of order 12; one-factorizations of r -regular graphs of order 12 are here classified for ... One-Factorizations of Degree 2n − 2 and Order 2n Uniqueness of a regular graph of degree 2n − 2 and order 2n follows directly from unique- ness of its complement g...

Ngày tải lên: 07/08/2014, 08:22

... of Panholzer and Prodinger for noncrossing trees and find a correspondence between a class of noncrossing trees, called proper noncrossing trees, and the set of symmetric ternary trees. The second ... plane trees T 1 and T 2 based on T: T 1 is the subtree containing the electr onic journal of combinatorics 13 (2006), #N12 3 Noncrossing Trees and Noncrossing Graphs...

Ngày tải lên: 07/08/2014, 13:21

... electronic journal of combinatorics 14 (2007), #N1 4 Maximum matchings in regular graphs of high girth Abraham D. Flaxman Microsoft Research Redmond, Washington, USA abie@microsoft.com Shlomo Hoory IBM ... The set of incidence vectors of the matchings of G have a convex hull which is equal to the polytope containing all x ∈ R E which satisfy the following the electronic...

Ngày tải lên: 07/08/2014, 13:21

... t). A join pair (G, t) is a join covered pair if each edge of G lies in a minimum t-join. Note that if T is a t-join in a join pair (G, t) and C is a circuit with more than half its edges in T , ... circuit containing P also contains all the other ears of X, including Q. By the inductive hypothesis, H has a comb T  H , equivalent to T ∩ EH, that has a balanced circuit containing e and...

Ngày tải lên: 07/08/2014, 15:23

... ∩ N(v)| to denote the number of neighbors of u (the degree of u) and the number of common neighbors of u and v, respectively. An n-vertex graph is called strongly regular, denoted SRG(n, r, , ... Characterization of Irregular (, à)-graphs In this section we prove that K 1 mK +1 is the only type of connected irregular (, à)- graphs. A nice interpretation of the result is th...

Ngày tải lên: 07/08/2014, 15:23

... in J. Graph Theory. the electronic journal of combinatorics 15 (2008), #R82 9 Irregularity strength of regular graphs Jakub Przybylo AGH University of Science and Technology Al. Mickiewicza ... of G is a map f : E(G) → {1, 2, . . . , w}. An irregularity strength of G, s(G), is the smallest w such that there is a w-weighting of G for which  e:u∈e f(e) =  e:v∈e f(e) for a...

Ngày tải lên: 07/08/2014, 21:20

... Press, 1987. the electronic journal of combinatorics 16 (2009), #N32 6 Skew Spectra of Oriented Graphs Bryan Shader Department of Mathematics University of Wyoming, Laramie, WY 82071-3036, USA email: ... σ. Proof. (Necessity) See the proof of Theorem 3.3 in [1]. (Sufficiency) Suppose Sp S (G σ ) = iSp(G) for any orientation σ. By Theorem 2.2, G is a bipartite graph. And so there...

Ngày tải lên: 07/08/2014, 21:21

... a (ℓ) uv is independent of u, v, provided that dist(u, v) = i ≤ k, and G is k-walk-regular. Conversely, suppose that G is k-walk-regular and consider the set of numbers of (u, v)-walks W = { a (0) i , ... th distance-regularity and walk-regularity, which we call k-walk-regularity. In particular, we present some algebraic characterizations of k-walk-regular graphs in terms of the so-calle...

Ngày tải lên: 07/08/2014, 21:21

... Classifications: 05C38, 05C40 Abstract We give a short proof of Gao and Richter’s th eorem that every circuit graph contains a closed walk visiting each vertex once or twice. 1 Introduction We only consider ... A note on circuit graphs Qing Cui Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016, P. R. China cui@nuaa.edu.cn Submitted: ... and Ric...

Ngày tải lên: 08/08/2014, 01:20

... graphs. We then give applications to random regular graphs of high degree and to the Platonic graphs. We use the latter r esults to study the Cheeger constants of arithmetic Riemann surfaces. Our ... Isoperimetric Numbers of Regular Graphs of High Degree with Applications to Arithmetic Riemann Surfaces Dominic Lanphier ∗ Department of Mathem...

Ngày tải lên: 08/08/2014, 14:23

... Douglas and Wang in [1] has also been t ested on classes of strongly regular graphs and of regular g raphs, where all non-isomorphic graphs were distinguished. Finding a pair of non-isomorphic strongly ... arbitrary graphs; in fact, he shows that k- boson quantum walks do not distinguish arbitrary graphs. However, the question of whether or not the procedure distinguishes al...

Ngày tải lên: 08/08/2014, 14:23