Resolvable decomposition of Kn∗

EveryH-decomposition ofKnhas a Nearly Resolvable Alternative

Let H be a fixed graph. An H-decomposition of Kn is a coloring of the edges of Kn such that every color class forms a copy of H. Each copy is called a member of the decomposition. The resolution number of an H-decomposition L of Kn, denoted χ(L), is the minimum number t such that the color classes (i.e. the members) of L can be partitioned into t subsets L1, . . . , Lt, where any two members be...

The linear 3-arboricity of Kn, n and Kn

A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted by lak(G), is the least number of linear k-forests needed to decompose G. In this paper, we completely determine lak(G) when G is a balanced complete bipartite graph Kn,n or a complete graph Kn, and k = 3. © 2007 Elsevier B.V. All rights reserved.

Bishellable drawings of Kn

The Harary-Hill conjecture, still open after more than 50 years, asserts that the crossing number of the complete graph Kn is H(n) = 1 4 ⌊ n 2 ⌋⌊ n− 1 2 ⌋⌊ n− 2 2 ⌋⌊ n− 3 2 ⌋ . Ábrego et al. [3] introduced the notion of shellability of a drawing D of Kn. They proved that if D is s-shellable for some s ≥ b 2 c, then D has at least H(n) crossings. This is the first combinatorial condition on a dr...

On the Defining Number of (2n - 2)-Vertex Colorings of Kn x Kn

TN , KN and KN Scattering : Skyrme Model vs . Experiment

_. -LWe present a comprehensive partial-wave analysis of the; processes rrN ---) &,I3 , KN + &B and TN + &., B in the 3-flavor Skyrme model, with c& an arbitrary pseudoscalar-octet meson and B a h’ octet or g’ decuplet baryon. Overall, we find good, poor, and mixed agreement, respectively, between the model and experiment for these three types of processes. We pay particular attention to assess...