Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On the injective chromatic number of graphs
Discrete Mathematics
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
Note: coloring the square of a K4-minor free graph
Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Injective coloring of planar graphs
Discrete Applied Mathematics
List injective coloring of planar graphs with girth 5, 6, 8
Discrete Applied Mathematics
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A k-coloring of a graph G=(V,E) is a mapping c:V驴{1,2,驴,k}. The coloring c is injective if, for every vertex v驴V, all the neighbors of v are assigned with distinct colors. The injective chromatic number 驴 i (G) of G is the smallest k such that G has an injective k-coloring. In this paper, we prove that every K 4-minor free graph G with maximum degree Δ驴1 has $\chi_{i}(G)\le \lceil \frac{3}{2}\Delta\rceil$ . Moreover, some related results and open problems are given.