Grzegorz Gutowski

Lower Bounds for On-line Graph Colorings

We propose two strategies for Presenter in on-line graph coloring games. The first one constructs bipartite graphs and forces any on-line coloring algorithm to use \(2\log _2 n - 10\) colors, where \(n\) is the number of vertices in the constructed graph. This is best possible up to an additive constant. The second strategy constructs graphs that contain neither \(C_3\) nor \(C_5\) as a subgraph and forces \(\varOmega (\frac{n}{\log n}^\frac{1}{3})\) colors. The best known on-line coloring algorithm for these graphs uses \(O(n^{\frac{1}{2}})\) colors.

A note on two-colorability of nonuniform hypergraphs

For a hypergraph

Lower Bounds for On-line Interval Coloring with Vector and Cardinality Constraints

H

Universal targets for homomorphisms of edge-colored graphs

, let

Optimal orientation on-line

q(H)

Mr. Paint and Mrs. Correct go fractional

denote the expected number of monochromatic edges when the color of each vertex in

The Partial Visibility Representation Extension Problem

H

Chip Games and Paintability

is sampled uniformly at random from the set of size 2. Let

The Slow-coloring Game on Sparse Graphs:

s_{\min}(H)

k

denote the minimum size of an edge in