# Search results for: Daphne Der-Fen Liu

Discussiones Mathematicae Graph Theory > 2017 > 38 > 1 > 5-26

Journal of Combinatorial Optimization > 2016 > 32 > 3 > 765-774

Discrete Applied Mathematics > 2014 > 167 > Complete > 45-51

Discrete Mathematics > 2013 > 313 > 18 > 1799-1804

Journal of Combinatorial Theory, Series A > 2013 > 120 > 1 > 159-163

Journal of Combinatorial Optimization > 2013 > 25 > 4 > 680-693

*D*be a set of positive integers. The distance graph generated by

*D*has all integers ℤ as the vertex set; two vertices are adjacent whenever their absolute difference falls in

*D*. We completely determine the chromatic number for the distance graphs generated by the sets

*D*={2,3,

*x*,

*y*} for all values

*x*and

*y*. The methods we use include the density of sequences with missing differences and the parameter...

Applied Mathematics Letters > 2012 > 25 > 5 > 898-901

Discrete Mathematics > 2012 > 312 > 8 > 1468-1475

Discrete Applied Mathematics > 2010 > 158 > 6 > 692-698

Journal of Graph Theory > 63 > 4 > 311 - 323

*k*‐fold coloring of a graph is a function that assigns to each vertex a set of

*k*colors, so that the color sets assigned to adjacent vertices are disjoint. The

*k*th chromatic number of a graph

*G*, denoted by χ

_{k}(

*G*), is the minimum total number of colors used in a

*k*‐fold coloring of

*G*. Let µ(

*G*) denote the Mycielskian of

*G*. For any positive integer

*k*, it holds that χ

_{k}(

*G*) + 1≤χ

_{k}(µ(

*G*))≤χ

_{k}(

*G*) +

*k*(W. Lin,...

Discrete Mathematics > 2009 > 309 > 12 > 3767-3773

Discrete Mathematics > 2008 > 308 > 24 > 5928-5936

European Journal of Combinatorics > 2008 > 29 > 7 > 1733-1743

Discrete Mathematics > 2008 > 308 > 7 > 1153-1164

Discrete Mathematics > 2004 > 285 > 1-3 > 335-340

^{t}(G), is defined recursively by M

^{0}(G)=G, and M

^{t}(G)=M(M

^{t}

^{-}

^{1}(G)) for t>=1. Let χ

_{c}(G) denote the circular chromatic number of G. We prove two main results: (1) If G has a universal vertex x, then χ

_{c}(M(G))=χ(M(G)) if χ

_{c}(G-x)>χ(G)-12...

Discrete Mathematics > 2001 > 232 > 1-3 > 163-169

Discrete Mathematics > 1996 > 161 > 1-3 > 197-205

_{T}(G), is the minimum span among all possible T-colorings...