Author:
Bhattacharya Sudatta,Dvorak Zdenek,Noorizadeh Fariba
Abstract
A \emph{$d$-dir} graph is an intersection graph of segments, where the segments have at most $d$ different slopes. It is easy to see that a $d$-dir graph with clique number $\omega$ has chromatic number at most $d\omega$. We study the chromatic number of $2$-dir graphs in more detail, proving that this upper bound is tight even in the fractional coloring setting.
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