Abstract
A proper vertex k-coloring C 1, C 2,…, C k of a graph G is called l- bounded ( l⩾0) if | C i ⧹ N( u)|⩽ l for each i=1,2,…, k and each vertex u∈ VG⧹ C i , where N( u) is the neighborhood of u. Let C( k, l) be the class of all graphs having an l-bounded k-coloring ( k⩾1 and l⩾0). We prove that every class C( k, l) has a finite forbidden induced subgraph characterization. This result implies the existence of polynomial algorithms for recognition of C( k, l). The set of all 14 minimal forbidden induced subgraphs for C(3,1) is found.
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