Structure Learning of H-Colorings

Structure Learning of H-colorings

We study the structure learning problem for graph homomorphisms, commonly referred to as Hcolorings, including the weighted case which corresponds to spin systems with hard constraints. The learning problem is as follows: for a fixed (and known) constraint graphH with q colors and an unknown graph G = (V,E) with n vertices, given uniformly random H-colorings of G, how many samples are required ...

H-Colorings of Large Degree Graphs

We consider the H-coloring problem on graphs with vertices of large degree. We prove that for H an odd cycle, the problem belongs to P. We also study the phase transition of the problem, for an infinite family of graphs of a given chromatic number, i.e. the threshold density value for which the problem changes from P to NP-complete. We extend the result for the case that the input graph has a l...

The Complexity of Parameterized H - Colorings

We survey recent results on the complexity of several versions of the H-coloring and the list-H-coloring problems that are amenable to param-eterization.

Counting H-Colorings of Partial k-Trees

Some Problems Involving H-colorings of Graphs

by John Alan Engbers For graphs G and H, an H-coloring of G, or homomorphism from G to H, is an edge-preserving map from the vertices of G to the vertices of H. H-colorings generalize such graph theory notions as proper colorings and independent sets. In this dissertation, we consider four questions involving H-colorings of graphs. Recently, Galvin [27] showed that the maximum number of indepen...