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...
DP-coloring is a generalization of list-coloring, which was introduced by Dvo谩k and Postle. Zhang showed that every planar graph with neither adjacent triangles nor 5-, 6-, 9-cycles is 3-choosable. Liu et al. showed that every planar graph without 4-, 5-, 6- and 9-cycles is DP-...
The minimum number of colors required for the coloring is called neighbor full sum distinguishing total chromatic number, denoted by ftndiΣ(G). In this paper, we show that ftndiΣ(G)≤Δ(G)+3 if G is a normal planar graph with girth g(G)≥6 and maximum degree Δ(G)≥10. This ...
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...
A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. This notion was recently introduced by Petruševski and Škrekovski, who proved that every planar graph admits an odd 9-coloring; they also conjecture...
planar graphs have been obtained in recent years.Now we introduce a famous conj ecture. Conjecture 1.1 For any graph G,(a) )(zi(G) :)( (G);(b) )(; (G) = )( (G) Part (a) of Conjecture 1.1 was formulated independently by a number of people,including ...
Note− A graph ‘G’ is said to be n-coverable if there is a vertex coloring that uses at most n colors, i.e., X(G) ≤ n. Region Coloring Region coloring is an assignment of colors to the regions of a planar graph such that no two adjacent regions have the same color. Two ...
Planar graphs with cycles of length neither 4 nor 6 are (2,0,0)(2,0,0)-colorable Let d1,d2,…,dkd1,d2,…,dk be k non-negative integers. A graph G is (d1,d2,…,dk)(d1,d2,…,dk)-colorable, if the vertex set of G can be partitioned into su... Y Wang,J Xu - ...
4) Edge Coloring of Planar Graphs 平面图的边染色5) edge colored graph 边染色图 1. If G is assigned such a coloring,then we say that G is an edge colored graph,or r-edge colored graph. 如果图G有这样的一个染色C,我们就称图G是一个边染色图,或r-边染色图,并用C(e)来表示边e的...
[k]-coloring an adjacent vertex distinguishing total coloring ofG.χa″(G)denotes the smallest valuekin such a coloring ofG. In this paper, by using the Combinatorial Nullstellensatz and the discharging method, we prove that if a planar graphGwith maximum degreeΔ≥8contains no adjacent 4-...