Báo cáo toán học: "On rainbow arithmetic progressions" ppsx

... 3 q }. This coloring is easy to show not to have any rainbow arithmetic progressions of length at least 3. It turns out that in order to force a rainbow AP(k) we need to ensure that for each color ... A 5 and i is odd, C otherwise. (4) the electronic journal of combinatorics 11 (2004), #R1 6 On rainbow arithmetic progressions Maria Axenovich Department of Mathematics Iowa State Univ...

Ngày tải lên: 07/08/2014, 08:20

... al. in [6]. An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. Clearly, if a graph is rainbow connected, then it is also connected. ... graph has a trivial edge coloring that makes it rainbow connected; just color each edge with a distinct color. Thus, one can properly define the rainbow connection number of a conn...

Ngày tải lên: 07/08/2014, 15:23

... 05C15 Abstract We derive sufficient conditions for the existence of rainbow cycles of all lengths in edge colourings of complete graphs. We also consider rainbow colorings of a certain class of trees. 1 Introduction Let ... K n is rainbow coloured if each edge of S is of a different colour. Various authors have considered the question of how large can b = b(n) be so that any b-bounded edge...

Ngày tải lên: 07/08/2014, 15:23

... u 2 +w 2 , u 3 +w 3 , u 1 , u 2 , u 3 ∈ V and w 1 , w 2 , w 3 ∈ W , are in arithmetic progression implies u 1 , u 2 , u 3 are in arithmetic progression: If (u 1 + w 1 ) + (u 3 + w 3 ) = 2(u 2 + w 2 ), then u 1 + ... Univ. Press, Cambridge, 1989. [8] R. Meshulam, On subsets of finite abelian groups with no 3 - term arithmetic progres- sions, J. Comb. Theory Ser. A. 71 (1995), 168-1 72. [9...

Ngày tải lên: 08/08/2014, 12:22

... absence of rainbow n-cycles and rainbow m-cycles implies the absence of rainbow (n + m − 2)-cycles. (For example, by this fact alone, the absence of rainbow 3-cycles implies there are no rainbow cycles ... immediate corollary guide us in our study of rainbow cycles. Lemma 1. If a coloring contains no rainbow n-cycles nor rainbow m-cycles, then it contains no rainbow (n + m −...

Ngày tải lên: 07/08/2014, 13:21

... however, for homogeneous arithmetic progressions (HAPs), the subfamily of arithmetic progressions containing 0. It turns out that there are extremely balanced colourings for such arithmetic progressions. ... it is not known whether the set of homogeneous arithmetic progressions have bounded discrepancy, there exist colourings (see [11]) for which the arithmetic progression {0, d, 2d...

Ngày tải lên: 07/08/2014, 21:20

... 3 A 1 T L T y’ y v v’ B 3sk + t 2sk + t Figure 2: A rainbow C k in Claim 1.3 and y ′ of colors from c(yLy ′ )\{ c( vy), c(v ′ y ′ )}, which together with V (P) induce a rainbow C k since colors of P are not ... 17 (2010), #R31 6 v y’ y T T L 2sk + t sk + t Figure 4: A rainbow C k in Claim 2.1 and Claim 2.2- 1.(1) v z x T T L t sk + t Figure 5: A rainbow C k in Claim 2.2-1.(2) (1) For...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 20/06/2014, 20:20