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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.  ...

Strong T-Coloring of Graphs

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
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.  ...

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.  ...

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.  ...

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] ).  ...

[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.  ...

[r, s, t; f]-COLORING OF GRAPHS

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.  ...

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.  ...

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.  ...

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.  ...

[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.  ...

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).  ...

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.  ...

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.  ...

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.  ...
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