On the difference between chromatic number and dynamic chromatic number of graphs

Ahadi, Arash; Akbari, S.; Dehghan, Ali; Ghanbari, M.

doi:10.1016/j.disc.2011.09.006

Cited by 33 publications

(36 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For every -regular graph , Alishahi [3] provided an upper bound with additional logarithmic term: 2 ( ) ≤ ( ) + 14.06 log + 1. Ahadi et al [4] posed the following conjecture, which generalizes Conjecture 1.…”

Section: Conjecturementioning

confidence: 88%

See 1 more Smart Citation

Dynamic choosability of triangle‐free graphs and sparse random graphs

Kim

2017

Journal of Graph Theory

View full text Add to dashboard Cite

Ther‐dynamic choosability of a graph G, written ch rfalse(Gfalse), is the least k such that whenever each vertex is assigned a list of at least k colors a proper coloring can be chosen from the lists so that every vertex v has at least min{dGfalse(vfalse),r} neighbors of distinct colors. Let ch(G) denote the choice number of G. In this article, we prove ch rfalse(Gfalse)≤false(1+o(1)false) ch false(Gfalse) when normalΔfalse(Gfalse)δfalse(Gfalse) is bounded. We also show that there exists a constant C such that the random graph G=G(n,p) with 6log(n)n

show abstract

Section: Conjecturementioning

confidence: 88%

“…Ahadi et al. posed the following conjecture, which generalizes Conjecture . Conjecture If G has maximum degree Δ and minimum degree δ, then

χ_{2} false(G false) \leq χ false(G false) + false⌈ \frac{Δ}{δ} false⌉ + 1

.…”

Section: Introductionmentioning

confidence: 89%

Dynamic choosability of triangle‐free graphs and sparse random graphs

Kim

2017

Journal of Graph Theory

View full text Add to dashboard Cite

show abstract

“…The 1-dynamic chromatic number of a graph G is equal to its chromatic number. The 2-dynamic chromatic number of a graph has been studied under the name dynamic chromatic number in Ahadi, Akbari, Dehghana, and Ghanbari (2012), Akbari, Ghanbari, andJahanbakam (2009, 2010, Alishahi (2012), Lai, Montgomery, and Poon (2003). There are many upper bounds and lower bounds for d (G) in terms of graph parameters.…”

Section: Public Interest Statementmentioning

confidence: 99%

δ-Dynamic chromatic number of Helm graph families

2016

View full text Add to dashboard Cite

An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v))| ≥ min r, d(v) , for each v ∈ V(G), where N(v) and d(v) denote the neighborhood and the degree of v, respectively. The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the -dynamic chromatic number of middle, total, and central of helm graph, where = min v∈V (G) d (v) .

show abstract

“…Initially, we define the following discharging rules (also see Figure 2) so that the charges are transferred among the elements in V (G × ) ∪ F (G × ). 1 3 to each of its incident true 3-face in G × ;…”

Section: Discharging: the Proof Of Theoremmentioning

confidence: 99%

“…Oum [16] in 2016. For other results on the dynamic coloring of graphs, we refer the reads to [1,4,8,9,10,13,18,19,20,21,24,26].…”

Section: Introductionmentioning

confidence: 99%

List edge and list total coloring of 1-planar graphs

2012

View full text Add to dashboard Cite

A graph is k-planar if it can be drawn in the plane so that each edge is crossed at most k times. Typically, the class of 1-planar graphs is among the most investigated graph families within the so-called "beyond planar graphs". A dynamic -list coloring of a graph is a proper coloring so that each vertex receives a color from a list of distinct candidate colors assigned to it, and meanwhile, there are at least two colors appearing in the neighborhood of every vertex of degree at least two. In this paper, we prove that each 1-planar graph has a dynamic 11-list coloring. Moreover, we show a relationship between the dynamic coloring of 1-planar graphs and the proper coloring of 2-planar graphs, which states that the dynamic (list) chromatic number of the class of 1-planar graphs is at least the (list) chromatic number of the class of 2-planar graphs.

show abstract

On the difference between chromatic number and dynamic chromatic number of graphs

Cited by 33 publications

References 7 publications

Dynamic choosability of triangle‐free graphs and sparse random graphs

Dynamic choosability of triangle‐free graphs and sparse random graphs

δ-Dynamic chromatic number of Helm graph families

List edge and list total coloring of 1-planar graphs

Contact Info

Product

Resources

About