Báo cáo toán học: "Symmetry Breaking in Graphs" pptx

... and φ cannot be distinguishing. This contradicts our assumption that φ is an r-distinguishing labeling. ✷ We remark that this proves that the largest integer in D(S 3 )is3,since the subgroups ... the goal is to minimize the number of colors used. Consequently we define the distinguishing number of a graph G by D(G)=min{r | G has a labeling that is r-distinguishing}. The original key problem...

Ngày tải lên: 07/08/2014, 06:20

... , proving (8). Inequality (9) follows easily, since, in fact, for every p>3, the function g (x)hasa local minimum at 0. ✷ 5 H-free graphs In this section we are going to prove the following ... (5), we obtain that (r −1)  n p +1  +  2n p +1  <n. Letting n →∞, we see that p ≥ r, contradicting the assumption and completing the proof. ✷ Maximizing independently each summand in (3...

Ngày tải lên: 07/08/2014, 08:20

... point, there must then be some point x common to all three lines. Fix a point x of the geometry. Now, each point is incident to m + 1 lines, so the probability that three or more points contain x ... that lines that contain q + 2 or more points are forbidden, although lines that containt q + 1 points are possible. The class L(q) adheres to other restrictions that elude our present interest, ....

Ngày tải lên: 07/08/2014, 13:21

... 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 class, at ... bound in Theorem 1 apply this estimate to the matrix A =(a u,v ) u∈V 1 ,v∈V 2 in which a u,v =1if u, v are adjacent and a u,v = 0 otherwise. Here M(G)=per(A). Since the function x! 1/x is inc...

Ngày tải lên: 07/08/2014, 06:22

... 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 can be determined if enough ... other cycles whose length is in C. In fact, the resulting graph G 0 must be in R(m 1 , ,m t ). Let B denote the average number of ways to apply a backward r-switching to G 1 if G 1 is...

Ngày tải lên: 07/08/2014, 08:20

... matching (or one-factor) of G is a subgraph of G in which each vertex has degree at most one. A basic question in combinatorial optimization is, “What is the size of a maximum matching in a given ... 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 journal of combinatori...

Ngày tải lên: 07/08/2014, 13:21

... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp. 599-611, 1998. [6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs, http://www.infres.enst.fr/∼lobstein/debutBIBidetlocdom.pdf [7] ... minimal r-twin-free graph for the induced subgraph relationship. Indeed, we have: the electronic journal of combinatorics 15 (2008), #N17 5 An r-twin-...

Ngày tải lên: 07/08/2014, 15:22

... Component evolution in random intersection graphs Michael Behrisch ∗ Institut f¨ur Informatik, Humboldt-Universit¨at zu Berlin, 10099 Berlin, Germany behrisch@informatik.hu-berlin.de Submitted: ... exp(c(ρ − 1)) (5) in the interval (0, 1). Thus the main complication in the proof is to overcome the limitations of the branching process which deals with an essentially unbounded domain in...

Ngày tải lên: 07/08/2014, 15:22

... graph G containing F i and any dominating set D in G, the set D has at least 9 vertices in V (F i ). If D contains neither x i nor y i , then by Claim 1 D must contain 3 vertices in each of V ... bound was proved in [2] by exploiting Reed’s techniques in [9] and examining some of the cases in Reed’s proof more carefully and adding a dis- charging argument. However, exploting Reed’...

Ngày tải lên: 07/08/2014, 15:22

... Cao, Integral trees of diameter R (3 ≤ R ≤ 6) (in Chinese), Heilongjiang Daxue Ziran Kexue Xuebao (2) (1988) 1-3, 95. [4] Z.F. Cao, Introductory Diophantine Equations (in Chinese), Haerbin Polytechnical University ... theory. Integral graphs in these classes were given by using number theory and computer search. In this paper, a new method of constructing fifteen in nite classes of inte...

Ngày tải lên: 07/08/2014, 15:22