$2\times n$ Grids have Unbounded Anagram-Free Chromatic Number

The oriented chromatic number of some grids

We define some infinite subfamily of hexagonal grids with the oriented chromatic number 5. We present an algorithm for oriented colouring of some hexagonal planar oriented grids. The algorithm uses BFS spanning tree of a subgraph of the dual graph of the grid and a homomorphism to some tournament of order 6. In general the difference between the number of colours given by the algorithm and the ...

The incidence chromatic number of toroidal grids

An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f , or the edge vw equals e or f . The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In...

On the oriented chromatic number of grids

Chromatic number of ISK4-free graphs

A graph G is said to be ISK4-free if it does not contain any subdivision of K4 as an induced subgraph. In this paper, we propose new upper bounds for chromatic number of ISK4-free graphs and {ISK4, triangle}-free graphs.

Anagram solving: does effort have an effect?

The purpose of these studies was to explore the role of effort in remembering anagrams and their solutions. In Experiment 1, we compared the effects on memory of copying words, typing them as solutions for easy anagrams, or typing them as solutions for difficult anagrams. Solving anagrams involved more effort than did simply typing words, as indexed by response time. However, this effort facili...