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T-colorings of graphs

Daphne Der-Fen Liu
1992 Discrete Mathematics  
., T-colorings of graphs, Discrete Mathematics 101 (1992) 203-212.  ...  The T-span of a T-coloring is defined as the difference of the largest and smallest colors used; the T-span of G, se,(G), is the minimum span over all T-colorings of G.  ...  Special thanks to Jerry for editorial supervision of this paper.  ... 
doi:10.1016/0012-365x(92)90603-d fatcat:4gegyqkp3rablkndzynj55b7bu

Strong T-Coloring of Graphs

A 𝑻-coloring of a graph 𝑮 = (𝑽,𝑬) is the generalized coloring of a graph.  ...  We define Strong 𝑻-coloring (S𝑻-coloring , in short), as a generalization of 𝑻-coloring as follows.  ...  In that model, for all the interference we have one fixed T see Ref( [4, 2] ). 𝑇-coloring of a graph 𝐺 = (𝑉, 𝐸) is the generalization coloring of a graph. Let 𝑇 ⊂ 𝑍 + ∪ {0} be any fixed set.  ... 
doi:10.35940/ijitee.l3575.1081219 fatcat:xo2lh2mtgjfohi32q2p3gclelq

Greedy T-colorings of graphs

Robert Janczewski
2009 Discrete Mathematics  
This paper deals with greedy T -colorings of graphs, i.e. T -colorings produced by the greedy (or first-fit) algorithm.  ...  is a function of T and the number of colors used, only.  ...  Introduction T -coloring of graphs is one of many graph-theoretic problems which arose as mathematical models for a practical problem.  ... 
doi:10.1016/j.disc.2008.01.049 fatcat:mr2li7mzmrc4bilwsb7lxtykoa

T-Colorings and T-Edge Spans of Graphs

Shin-Jie Hu, Su-Tzu Juan, Gerard J. Chang
1999 Graphs and Combinatorics  
The edge span of a T-coloring f is the maximum value of j f x À f yj over all edges xy, and the T-edge span of a graph G is the minimum value of the edge span of a T-coloring of G.  ...  Suppose G is a graph and T is a set of non-negative integers that contains 0.  ...  a T-coloring of G.  ... 
doi:10.1007/s003730050063 fatcat:vm2jldfsvrg33e7p3ez2ngsaxy

Finite-dimensional T-colorings of graphs

Roger K. Yeh
2001 Theoretical Computer Science  
This article proposes ÿnite-dimensional T -colorings on simple graphs. The ordinary T -coloring will be the one-dimensional version of our T -colorings.  ...  The edge span of a T (d; p)-coloring f on a graph G; esp T (f; d; p), is the maximum value of {||f(u) − f(v)||p : {u; v} ∈ E(G)}.  ...  Recall the span of a graph G is the minimum value of max(f)−min(f) among all T -colorings f on G. The exact value of sp T (K n ) has been found for several classes of T -sets (cf. [4] ).  ... 
doi:10.1016/s0304-3975(00)00249-8 fatcat:3cv27px3jbgynjamdm75zgpdpu

[r,s,t]-Colorings of graphs

Arnfried Kemnitz, Massimiliano Marangio
2007 Discrete Mathematics  
This is an obvious generalization of all classical graph colorings since c is a vertex coloring if r = 1, s = t = 0, an edge coloring if s = 1, r = t = 0, and a total coloring if r = s = t = 1, respectively  ...  Given non-negative integers r, s, and t, an [r, s, t]-coloring of a graph s for every two adjacent edges e i , e j , and |c(v i ) − c(e j )| t for all pairs of incident vertices and edges, respectively  ...  Therefore, let a 2 and c be an [r, s, t]-coloring of a graph G with r,s,t (G) colors.  ... 
doi:10.1016/j.disc.2006.06.030 fatcat:wrkwed5kfvdnjmetmkwc5eal7u


Yong Yu, Guizhen Liu
2011 Journal of the Korean Mathematical Society  
Let f be a function which assigns a positive integer f (v) to each vertex v ∈ V (G), let r, s and t be non-negative integers.  ...  Zhang and Liu [7, 8, 9] studied the f -coloring of graphs and got many interesting results. Kemnitz and Marangio [6] studied the [r, s, t]-coloring of a graph G.  ...  Then Theorem 2. 7 . 7 Let G be a graph and let r, s, t, f be defined as in the definition of [r, s, t; f ]-coloring.  ... 
doi:10.4134/jkms.2011.48.1.105 fatcat:wlzis5koincwxof4kabfoiniue

Facial [r.s,t]-colorings of plane graphs

Július Czap, Stanislav Jendrol', Peter Šugerek, Juraj Valiska
2018 Discussiones Mathematicae Graph Theory  
The facial [r, s, t]-chromatic number χ r,s,t (G) of G is defined to be the minimum k such that G admits a facial [r, s, t]-coloring with colors 1, . . . , k.  ...  Given nonnegative integers r, s, and t, a facial [r, s, t]-coloring of a plane graph G = (V, E) is a mapping f : V ∪ E → {1, . . . , k} such that |f (v 1 ) − f (v 2 )| ≥ r for every two adjacent vertices  ...  Results concerning [r, s, t]-colorings of graphs can be found in [7, 8, 16-20, 22, 25] . In this paper we deal with a relaxation of the [r, s, t]-coloring for plane graphs.  ... 
doi:10.7151/dmgt.2135 fatcat:lf4obr7langxtk4ptj246c7e4e

New results in t-tone coloring of graphs [article]

Daniel W. Cranston, Jaehoon Kim, William B. Kinnersley
2011 arXiv   pre-print
A t-tone k-coloring of G assigns to each vertex of G a set of t colors from {1,..., k} so that vertices at distance d share fewer than d common colors.  ...  The t-tone chromatic number of G, denoted τ_t(G), is the minimum k such that G has a t-tone k-coloring.  ...  Given a graph G and a t ′ -tone coloring of G, we arbitrarily discard t ′ − t colors from each label of G.  ... 
arXiv:1108.4751v1 fatcat:r4qamkdqzvhpfaijp2zahne2x4

New Results in t-Tone Coloring of Graphs

Daniel Cranston, Jaehoon Kim, William Kinnersley
2013 Electronic Journal of Combinatorics  
A $t$-tone $k$-coloring of $G$ assigns to each vertex of $G$ a set of $t$ colors from $\{1,\dots,k\}$ so that vertices at distance $d$ share fewer than $d$ common colors.  ...  The $t$-tone chromatic number of $G$, denoted $t(G)$, is the minimum $k$ such that $G$ has a $t$-tone $k$-coloring.  ...  Given a graph G and a t -tone coloring of G, we arbitrarily discard tt colors from each label of G.  ... 
doi:10.37236/2710 fatcat:codqbegtl5ayzjtohd2kyqtgdu

[r,s,t]-coloring of trees and bipartite graphs

Lyes Dekar, Brice Effantin, Hamamache Kheddouci
2010 Discrete Mathematics  
Thus, an [r, s, t]-coloring is a generalization of the total coloring and the classical vertex and edge colorings of graphs.  ...  Marangio, [r, s, t]colorings of graphs, Discrete Mathematics 307 (2) (2007) 199-207], channel assignment problem [F. Bazzaro, M. Montassier, A.  ...  Thus, an [r, s, t]-coloring is a generalization of the total coloring and the classical vertex and edge colorings of graphs.  ... 
doi:10.1016/j.disc.2008.09.021 fatcat:u46ule7xmffkhoumckpj4lqeeu

The edge span of T-coloring on graph Cnd

Yongqiang Zhao, Wenjie He, Rongrong Cao
2006 Applied Mathematics Letters  
A T -coloring of G is a nonnegative integer function | over all edges xy, and the T -edge span of G, esp T (G), is the minimum edge span over all T -colorings of G.  ...  Suppose G is a graph and T is a set of nonnegative integers that contains 0.  ...  Given a graph G and a T -set T , the order of a T -coloring f of G is the number of distinct values of f (x), x ∈ V (G).  ... 
doi:10.1016/j.aml.2005.08.016 fatcat:wkwulyokwzaqxlj4zi2p7ahd4q

The Packing Coloring of Distance Graphs D(k,t) [article]

Jan Ekstein, Přemysl Holub, Olivier Togni
2013 arXiv   pre-print
We also give some upper and lower bounds for χ_ρ(D(k, t)) with small k and t. Keywords: distance graph; packing coloring; packing chromatic number  ...  For k < t we study the packing chromatic number of infinite distance graphs D(k, t), i.e. graphs with the set of integers as vertex set and in which two distinct vertices i, j ∈ are adjacent if and only  ...  by the Ministry of Education, Youth and Sports of the Czech Republic, is highly appreciated.  ... 
arXiv:1302.0721v1 fatcat:ykr7i5ni5bbevgf6cpct5xemly

On t-relaxed 2-distant circular coloring of graphs [article]

Dan He, Wensong Lin
2019 arXiv   pre-print
, or simply a (k/2,t)^*-coloring of G.  ...  For any outerplanar graph G, e show that all outerplanar graphs are (5/2,4)^*-colorable, we prove that there is no fixed positive integer t such that all outerplanar graphs are (4/2,t)^*-colorable.  ...  Since f is a (4, t)-defective coloring of graph G, it is easy to see that g is a ( 4 2 , t) * -coloring of graph G * t . Now suppose G * t has a ( 4 2 , t) * -coloring g.  ... 
arXiv:1910.07321v1 fatcat:6a4tctxxtzbb3nwln6zbsbssuy

T-colorings of graphs: recent results and open problems

Fred S. Roberts
1991 Discrete Mathematics  
., T-colorings of graphs: re---* bb,Ic results and open problems, Discrete Mathematics 93 (1991) 229-24s. Suppose G is a graph and T is a set of nonnegative integers.  ...  A T-coloring of G is an assignment of a positive integer f(x) to each vertex x of G so that if x and y are joined by an edge of G, then V(X) -f (y)l is not in T.  ...  Acknowledgements The author gratefully acknowledges the support of Air Force Office of Scientific Research grants AFOSR-85-0271, AFOSR-89-0512, and AFOSR-!%I-0008 to Rutgers University.  ... 
doi:10.1016/0012-365x(91)90258-4 fatcat:6bmqbfltm5cbloaeembmxryhku
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