List improper colorings of planar graphs with prescribed girth
Discrete Mathematics
A Grötzsch-Type Theorem for List Colourings with Impropriety One
Combinatorics, Probability and Computing
List Improper Colourings of Planar Graphs
Combinatorics, Probability and Computing
Graph Theory With Applications
Graph Theory With Applications
Every toroidal graph without adjacent triangles is (4, 1)*-choosable
Discrete Applied Mathematics
Every toroidal graph without adjacent triangles is (4, 1)*-choosable
Discrete Applied Mathematics
A (3,1)*-choosable theorem on toroidal graphs
Discrete Applied Mathematics
On (3,1 )*-choosability of planar graphs without adjacent short cycles
Discrete Applied Mathematics
| Hi-index | 0.04 |
A list-assignment L to the vertices of G is an assignment of a set L(v) of colors to vertex v for every v@?V(G). An (L,d)^*-coloring is a mapping @f that assigns a color @f(v)@?L(v) to each vertex v@?V(G) such that at most d neighbors of v receive color @f(v). A graph is called (k,d)^*-choosable, if G admits an (L,d)^*-coloring for every list assignment L with |L(v)|=k for all v@?V(G). In this note, it is proved that every plane graph, which contains no 4-cycles and l-cycles for some l@?{8,9}, is (3,1)^*-choosable.