Graph coloring satisfying restraints

摘要: Abstract For an integer k ⩾2, a proper k-restraint on graph G is function from the vertex set of to -colors. A amenably k-colorable if, for each nonconstant -restraint r , there -coloring c with ( v )≠ ) . amenable if it -colorable and chromatic number any ≠3, are infinitely many -critical graphs. ⩾ 3, we use construction B. Toft graphs associate finite hypergraph. Some constructions given. We also consider related property—being strongly critical —that satisfied by graphs, including complete amenable, but converse not always true. The Dirac join operation preserves both amenability property. In addition, Hajos applied single edge in two yields graph. However, ⩾5, which copies amenable.