Planar graphinjective coloringlist coloringAn injective [Formula: see text]-coloring of a graph [Formula: see text] is called injective if any two vertices joined by a path of length two get different colors. A graph [Formula: see text] is injectively [Formula: see text]-choosable if for...
A graph [Formula: see text] is injectively [Formula: see text]-choosable if for any color list [Formula: see text] of admissible colors on [Formula: see text] of size [Formula: see text] it allows an injective coloring [Formula: see text] such that [Formula: see text] whenever [...
Euler’s formula links girth and maximum average degree in the case of planar graphs. Lemma 1 Folklore For every planar graph , . By Lemma 1, Theorem 4 implies Theorem 3. An injective k-coloring [17] of is a (not necessarily proper) coloring of the vertices of with colors such that ...
planar graphinjective coloring klist coloringActa Mathematicae Applicatae Sinica, English Series - A k-coloring of a graph G is a mapping c: V(G) → {1, 2, , k}. The coloring c is called injective if any two vertices have a common...doi:10.1007/s10255-022-1103-7Jiansheng Cai...
Let L be a color list of G, if G has an injective coloring c such that c(v) ∈ L(v), ∀v ∈ V(G), then we call c an injective L-coloring of G. If for any color list L, such that |L(v)| ≥ k, G has an injective L-coloring, then G is said to be injective k-...
Planar graphCycleGrithList injective coloringAn injective k-coloring of graph G is a mapping c : V(G) -> {1,2, . . . , k}, such that c(u) not equal c(v) for any two vertices u, v is an element of V(G), whenever u, v have a common neighbor. If G has an injective k...
H.-Y. Chen and J.-L. Wu. List injective coloring of planar graphs with girth g ≥ 6. Discrete Math., 339(12):3043-3051, 2016.Bu Yuehua, Iai kai. List injective coloring of planar graphs with girth 5,6,8 original[ J]. Research Article Discrete Applied Mathematics, 2013161:1367-...
More generally, we show that graphs with maximum average degree less than 3 and Δ≥ 17 are list 2-distance (Δ + 2)-colorable. The proof can be transposed to list injective (Δ + 1)-coloring.Marthe BonamyBenjamin LévêqueAlexandre Pinlou...
Planar graphgirthinjective coloringlist coloringAn injective k -coloring of a graph G is a mapping c: V ( G ) → { 1 , 2 , … , k } such that c ( u ) ≠ c ( v ) whenever u , v have a common neighbor in G . A list assignment of a graph G is a mapping L that ...
An injective-k coloring of a graph G is a mapping cV(G) → {1, 2, …, k}, such that c(u) ≠ c(v) for each u, v ∈ V(G), whenever u, v have a common neighbor in G. If G has an injective-k coloring, then...