Bounds on Edge Colorings with Restrictions on the Union of Color Classes

The authors consider constrained proper edge colorings of the following type: Given a positive integer j and a family F of connected graphs on three or more vertices, they require that the subgraph formed by the union of any j color classes has no copy of any member of F. This generalizes some well-known types of colorings such as acyclic edge colorings, distance-2 edge colorings, low treewidth edge colorings, etc. For such a generalization of restricted colorings, the authors obtain an upper bound of ... on the minimum number of colors used in such a coloring. Their proof is based on probabilistic arguments. In particular, they obtain O(d) upper bounds for proper edge colorings with various interesting restrictions placed on the union of color classes. Some ways of improving the bounds are sketched. (ProQuest: ... denotes formulae/symbols omitted.)