We analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree (log n/ log log n), ...
Martin E. Dyer, Abraham D. Flaxman, Alan M. Frieze...
In order to perform an average-case analysis for specific input distributions one needs to derive and understand properties of a 'typical' input instance. In the case of...
We show efficient algorithms for edge-coloring planar graphs. Our main result is a linear-time algorithm for coloring planar graphs with maximum degree with max{, 9} colors. Thus...
: We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured b...