Kittikorn Nakprasit

Equitable colorings of planar graphs with maximum degree at least nine

In [Y. Zhang, H.P. Yap, Equitable colorings of planar graphs, J. Combin. Math. Conbin. Comput. 27 (1998) 97-105], Zhang and Yap essentially proved that each planar graph with maximum degree @D at least 13 has an equitable @D-coloring. In this paper, we proved that each planar graph in various classes has an equitable @D-coloring, especially planar graphs with maximum degree 9, 10, 11, and 12. Consequently, each planar graph with maximum degree @D at least 9 has an equitable @D-coloring.

Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings

Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and Zhang and Su (2007) as special cases. We also apply our method to find a common element to the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem. Finally, we propose an iteration to obtain convergence theorems for a continuous monotone mapping.

The Game Coloring Number of Planar Graphs with a Specific Girth

Let

Graphs with Bounded Maximum Average Degree and Their Neighbor Sum Distinguishing Total-Choice Numbers

\mathrm{col_g}(G)

Note: A note on the strong chromatic index of bipartite graphs

colg(G) be the game coloring number of a given graph G. Define the game coloring number of a family of graphs

Equitable colorings of planar graphs without short cycles

\mathcal {H}