Reorientations of covering graphs
Discrete Mathematics
On conflict-free coloring of points and simple regions in the plane
Proceedings of the nineteenth annual symposium on Computational geometry
Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Coloring Axis-Parallel Rectangles
Computational Geometry and Graph Theory
Notes: Coloring axis-parallel rectangles
Journal of Combinatorial Theory Series A
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Let $P=(X,\le)$ be a finite partially ordered set. That is, $X$ is a finite ground set and $\le$ is a partial ordering on $X$ (a reflexive, transitive, and weakly antisymmetric relation). An $x\in X$ is an immediate predecessor of a $y\in X$ if $xHasse diagram $H(P)$ is the undirected graph with vertex set $X$ and with $\{x,y\}$ forming an edge if $x$ is an immediate predecessor of $y$ or if $y$ is an immediate predecessor of $x$. We denote bya $\alpha(H(P))$ the independence number of the Hasse diagram, that is, the maximum possible size of a subset $I\subseteq X$ such that no element of $I$ is an immediate predecessor (in $P$) of another element of $I$. This quantity should not be confused with the maximum size of an antichain in $P$, which is sometimes denoted by $\alpha(P)$.