Every planar graph without 5-cycles and K 4 − and adjacent 4-cycles is ( 2, 0, 0 )-colorable

Let $$c_{1},c_{2},\ldots ,c_{k}$$c1,c2,ź,ck be k non-negative integers. A graph G is $$(c_{1},c_{2},\ldots ,c_{k})$$(c1,c2,ź,ck)-colorable if the vertex set can be partitioned into k sets $$V_{1},V_{2},\ldots ,V_{k}$$V1,V2,ź,Vk such that for every $$i,1\...

Let d 1 , d 2 , , d k be k nonnegative integers. A graph G = ( V , E ) is ( d 1 , d 2 , , d k ) -colorable, if the vertex set V of G can be partitioned into subsets V 1 , V 2 , , V k such that the subgraph G V i induced by V i has maximum degree at most ...

A ( c 1 , c 2 , , c k ) -coloring of G is a mapping : V ( G ) { 1 , 2 , , k } such that for every i , 1 i k , G V i has maximum degree at most c i , where G V i denotes the subgraph induced by the vertices colored i . Borodin and Raspaud conjecture that ...