Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Mathematics
Recursive Linear Bounds For The Vertex Chromatic Number Of The Pancake Graph, Aldrich Ellis C. Asuncion, Renzo Roel P. Tan, Christian Chan Shio, Kazushi Ikeda
Recursive Linear Bounds For The Vertex Chromatic Number Of The Pancake Graph, Aldrich Ellis C. Asuncion, Renzo Roel P. Tan, Christian Chan Shio, Kazushi Ikeda
Mathematics Faculty Publications
The pancake graph has been the subject of research. While studies on the various aspects of the graph are abundant, results on the chromatic properties may be further enhanced. Revolving around such context, the paper advances an alternative method to produce novel linear bounds for the vertex chromatic number of the pancake graph. The accompanying demonstration takes advantage of symmetries inherent to the graph, capturing the prefix reversal of subsequences through a homomorphism. Contained within the argument is the incorporation of known vertex chromatic numbers for certain orders of pancake graphs, rendering tighter bounds possible upon the release of new …
On Twin Edge Colorings In M-Ary Trees, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
On Twin Edge Colorings In M-Ary Trees, Jayson D. Tolentino, Reginaldo M. Marcelo, Mark Anthony C. Tolentino
Mathematics Faculty Publications
Let k ≥ 2 be an integer and G be a connected graph of order at least 3. A twin k-edge coloring of G is a proper edge coloring of G that uses colors from ℤk and that induces a proper vertex coloring on G where the color of a vertex v is the sum (in ℤk) of the colors of the edges incident with v. The smallest integer k for which G has a twin k-edge coloring is the twin chromatic index of G and is denoted by χ′t(G …