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T-colorings of graphs

1992
*
Discrete Mathematics
*

.,

doi:10.1016/0012-365x(92)90603-d
fatcat:4gegyqkp3rablkndzynj55b7bu
*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

doi:10.35940/ijitee.l3575.1081219
fatcat:xo2lh2mtgjfohi32q2p3gclelq
*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. ...##
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Greedy T-colorings of graphs

2009
*
Discrete Mathematics
*

This paper deals with greedy

doi:10.1016/j.disc.2008.01.049
fatcat:mr2li7mzmrc4bilwsb7lxtykoa
*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. ...##
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T-Colorings and T-Edge Spans of Graphs

1999
*
Graphs and Combinatorics
*

The edge span

doi:10.1007/s003730050063
fatcat:vm2jldfsvrg33e7p3ez2ngsaxy
*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. ...##
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Finite-dimensional T-colorings of graphs

2001
*
Theoretical Computer Science
*

This article proposes ÿnite-dimensional

doi:10.1016/s0304-3975(00)00249-8
fatcat:3cv27px3jbgynjamdm75zgpdpu
*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] ). ...##
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[r,s,t]-Colorings of graphs

2007
*
Discrete Mathematics
*

This is an obvious generalization

doi:10.1016/j.disc.2006.06.030
fatcat:wrkwed5kfvdnjmetmkwc5eal7u
*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*. ...##
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[r, s, t; f]-COLORING OF GRAPHS

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

doi:10.4134/jkms.2011.48.1.105
fatcat:wlzis5koincwxof4kabfoiniue
*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*. ...##
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Facial [r.s,t]-colorings of plane graphs

2018
*
Discussiones Mathematicae Graph Theory
*

The facial [r, s,

doi:10.7151/dmgt.2135
fatcat:lf4obr7langxtk4ptj246c7e4e
*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*. ...##
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New results in t-tone coloring of graphs
[article]

2011
*
arXiv
*
pre-print

A

arXiv:1108.4751v1
fatcat:r4qamkdqzvhpfaijp2zahne2x4
*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. ...##
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New Results in t-Tone Coloring of Graphs

2013
*
Electronic Journal of Combinatorics
*

A $

doi:10.37236/2710
fatcat:codqbegtl5ayzjtohd2kyqtgdu
*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. ...##
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[r,s,t]-coloring of trees and bipartite graphs

2010
*
Discrete Mathematics
*

Thus, an [r, s,

doi:10.1016/j.disc.2008.09.021
fatcat:u46ule7xmffkhoumckpj4lqeeu
*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*. ...##
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The edge span of T-coloring on graph Cnd

2006
*
Applied Mathematics Letters
*

A

doi:10.1016/j.aml.2005.08.016
fatcat:wkwulyokwzaqxlj4zi2p7ahd4q
*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). ...##
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The Packing Coloring of Distance Graphs D(k,t)
[article]

2013
*
arXiv
*
pre-print

We also give some upper and lower bounds for χ_ρ(D(k,

arXiv:1302.0721v1
fatcat:ykr7i5ni5bbevgf6cpct5xemly
*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. ...##
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On t-relaxed 2-distant circular coloring of graphs
[article]

2019
*
arXiv
*
pre-print

, or simply a (k/2,

arXiv:1910.07321v1
fatcat:6a4tctxxtzbb3nwln6zbsbssuy
*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. ...##
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T-colorings of graphs: recent results and open problems

1991
*
Discrete Mathematics
*

.,

doi:10.1016/0012-365x(91)90258-4
fatcat:6bmqbfltm5cbloaeembmxryhku
*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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