  We introduce and examine the {\em Holiday Gathering Problem} which models the
difficulty that couples have when trying to decide with which parents should
they spend the holiday. Our goal is to schedule the family gatherings so that
the parents that will be {\em happy}, i.e.\ all their children will be home
{\em simultaneously} for the holiday festivities, while minimizing the number
of consecutive holidays in which parents are not happy.
  The holiday gathering problem is closely related to several classical
problems in computer science, such as the {\em dining philosophers problem} on
a general graph and periodic scheduling,and has applications in scheduling of
transmissions made by cellular radios. We also show interesting connections
between periodic scheduling, coloring, and universal prefix free encodings.
  The combinatorial definition of the Holiday Gathering Problem is: given a
graph $G$, find an infinite sequence of independent-sets of $G$. The objective
function is to minimize, for every node $v$, the maximal gap between two
appearances of $v$. In good solutions this gap depends on local properties of
the node (i.e., its degree) and the the solution should be periodic, i.e.\ a
node appears every fixed number of periods. We show a coloring-based
construction where the period of each node colored with the $c$ is at most
$2^{1+\log^*c}\cdot\prod_{i=0}^{\log^*c} \log^{(i)}c$ (where $\log^{(i)}$ means
iterating the $\log$ function $i$ times). This is achieved via a connection
with {\it prefix-free encodings}. We prove that this is the best possible for
coloring-based solutions. We also show a construction with period at most $2d$
for a node of degree $d$.
