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T-colorings of graphs
1992
Discrete Mathematics
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., 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
2019
VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
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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
2009
Discrete Mathematics
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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
1999
Graphs and Combinatorics
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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
2001
Theoretical Computer Science
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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
2007
Discrete Mathematics
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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
[r, s, t; f]-COLORING OF GRAPHS
2011
Journal of the Korean Mathematical Society
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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
2018
Discussiones Mathematicae Graph Theory
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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]
2011
arXiv
pre-print
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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
2013
Electronic Journal of Combinatorics
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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 t − t colors from each label of G. ...
doi:10.37236/2710
fatcat:codqbegtl5ayzjtohd2kyqtgdu
[r,s,t]-coloring of trees and bipartite graphs
2010
Discrete Mathematics
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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
2006
Applied Mathematics Letters
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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]
2013
arXiv
pre-print
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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]
2019
arXiv
pre-print
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, 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
1991
Discrete Mathematics
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., 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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