Brooksʼ Theorem for generalized dart graphs - Kochol, Martin; Škrekovski, Riste (Information processing letters, 2012)
The well-known Brooksʼ Theorem says that each graph G of maximum degree k ⩾ 3 is k-colorable unless G = K k + 1 . We generalize this theorem by allowing higher degree vertices with prescribed types of neighborhood. ► Generalization of Brooks Theorem for ( k , s ) -dart graphs. ► Linear algorithm for ( k + 1 ) -coloring of ( k , s ) -dart graphs with s not greater then k. ► NP-completeness for ( k + 1 ) -coloring of ( k , s ) -dart graphs with s greater then k.