Note on property M(k) of some complete multipartite graphs
We study the unique list coloring problem for a class of complete multipartite graphs. It is known that graphs K1?3,r K 1 ? 3 , r and K1?r,3 K 1 ? r , 3 have the property M(3) M ( 3 ) . It is known that graphs K1?5,r K 1 ? 5 , r and K1?r,5 K 1 ? r , 5 have the property M(4) M ( 4 ) . We show that graphs K1?r,(2k?3) K 1 ? r , ( 2 k ? 3 ) and K1?(2k?3),r K 1 ? ( 2 k ? 3 ) , r have the property M(k) M ( k ) .
complete multipartite graphs list coloring property m(k) m ( k ) m(k) m ( k ) m(k) m ( k ) m ( k ) graph algorithm