Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Online Ramsey Games for more than two colors   Consider the following one-player game played on an initially empty graph
with $n$ vertices. At each stage a randomly selected new edge is added and the
player must immediately color the edge with one of $r$ available colors. Her
objective is to color as many edges as possible without creating a
monochromatic copy of a fixed graph $F$.
  We use container and sparse regularity techniques to prove a tight upper
bound on the typical duration of this game with an arbitrary, but fixed, number
of colors for a family of $2$-balanced graphs. The bound confirms a conjecture
of Marciniszyn, Sp\"ohel and Steger and yields the first tight result for
online graph avoidance games with more than two colors.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin