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A Bound on the Total Chromatic Number
1998
Combinatorica
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In particular, we show that for su ciently large, the total chromatic number of such a graph is at most + 10 26 . The proof is probabilistic. ...
We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. ...
The total chromatic number, 00 (G) is the least number of colours required for a total colouring of G. ...
doi:10.1007/pl00009820
fatcat:q2yt4mkiuzbhxj3a3zjkgki6rm
A new upper bound for total colourings of graphs
1995
Discrete Mathematics
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We give a new upper bound on the total chromatic number of a graph. This bound improves the results known for some classes of graphs. ...
The bound is stated as follows: ZT ~< Z~ + L l3 ~ J + 2, where Z is the chromatic number, Z~ is the edge chromatic number (chromatic index) and ZT is the total chromatic number. ...
The chromatic number •(G), edge chromatic number ze(G), total chromatic number ~T(G) is the least number of colours in a vertex, edge, total colouring of G, respectively. ...
doi:10.1016/0012-365x(94)00219-9
fatcat:4hruj5izt5h7tlcfinnred3rby
Local super antimagic total face coloring of planar graphs
2019
IOP Conference Series: Earth and Environment
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Acknowledgement We are grateful for a wonderful support from Universitas Islam Negeri Syarif Hidayatullah Jakarta and CGANT -University of Jember in 2018. ...
We combine an upper bound value with a lower bound value. We get γ latf (L n ) = 2. 2.4. The local super antimagic total face chromatic number of circular ladder graph Let n ≥ 3 be a natural number. ...
The local super antimagic total face chromatic number of ladder graph Let n ≥ 2 be a natural number. ...
doi:10.1088/1755-1315/243/1/012117
fatcat:uiw7yu5qwfcm3g5quohtttgl5a
Page 53 of Mathematical Reviews Vol. , Issue 2002A
[page]
2002
Mathematical Reviews
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On the total chromatic number of Steiner systems. ...
Summary: “In this work we give a new lower bound on the
chromatic number of a Mycielski graph M;. ...
Page 48 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
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We also show that the total choice number of a graph of maximum degree 2 is equal to its total chromatic number.”
2000a:05082 05C15
Kayll, P. ...
Enomoto, Hornak, and Jendrol’ [“Cyclic chromatic number of 3-connected plane graphs”, submitted] obtained the above sharp bound under weaker restrictions on k. ...
Tight bounds on the chromatic sum of a connected graph
1989
Journal of Graph Theory
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In this article we determine tight bounds on the chromatic sum of a connected graph with e edges, ...
The chromatic sum of a graph is introduced in the dissertation of Ewa Kubicka. It is the smallest possible total among all proper colorings of G using natural numbers. ...
ACKNOWLEDGMENT The research of P. J. M. and A. J. S. was supported in part by the Office of Naval Research Contract N00014-86-K-0566. ...
doi:10.1002/jgt.3190130310
fatcat:rrkc277lt5bm3hte2wld426ita
Two-floor buildings need eight colors
2015
Journal of Graph Algorithms and Applications
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We also discuss bounds on the chromatic number of the adjacency graph of general arrangements of 3-dimensional parallelepipeds according to geometrical measures of the parallelepipeds (side length, total ...
In the case each parallelepiped is within one floor, a direct application of the Four-Colour Theorem yields that the adjacency graph has chromatic number at most 8. ...
The third author thanks Louigi Addario-Berry, Frédéric Havet, Ross Kang, Colin McDiarmid and Tobias Müller for stimulating discussions on the topic of this paper during a stay in Oxford, in 2005. ...
doi:10.7155/jgaa.00344
fatcat:oulq75r4zjeorjonqj7sqwr3wi
Total Dominator Colorings In Paths
[article]
2012
Zenodo
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Determining the total dominator chromatic number in paths. ...
Next,we obtain a bound for td-chromatic number through the total domination number and chromatic number. Theorem 2.7.Let G be any graph with (G) 1. ...
The total dominator
chromatic number (td-chromatic number) of G is defined as minimum number of
colors needed in a total dominator coloring of G and is denoted by td (G). ...
doi:10.5281/zenodo.9127
fatcat:3jgga2tdbnhzbbufuyjcr2io3e
Page 4149 of Mathematical Reviews Vol. , Issue 93h
[page]
1993
Mathematical Reviews
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For k = 3, the k-cyclic chromatic number coincides with the chromatic number of the graph. For k = 4, it is at most 6 and this upper bound is tight. ...
It is proved that a graph G with 2n vertices and maximum degree 2n—2 has total chromatic number 27 — 1 unless the complement of G is K2U Kj 2n-3, in which case the total chromatic number is 27. ...
Page 6090 of Mathematical Reviews Vol. , Issue 2001I
[page]
2001
Mathematical Reviews
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The lower bound for the chromatic number of R” has been (1.207+ 0(1))". The paper improves the lower bound to (1.239 + o(1))”. ...
On the other hand, for every number f; > fo, the interval from fp to ¢; contains a chromatic root of a graph with a Hamiltonian path. ...
Two floor building needing eight colors
[article]
2014
arXiv
pre-print
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We also discuss bounds on the chromatic number of the adjacency graph of general arrangements of 3-dimensional parallelepipeds according to geometrical measures of the parallelepipeds (side length, total ...
In the case each parallelepiped is within one floor, a direct application of the Four-Colour Theorem yields that the adjacency graph has chromatic number at most 8. ...
The third author thanks Louigi Addario-Berry, Frédéric Havet, Ross Kang, Colin McDiarmid and Tobias Müller for stimulating discussions on the topic of this paper during a stay in Oxford, in 2005. ...
arXiv:1405.6620v1
fatcat:iejlsbhfibcybalo4up3u35zai
Clique Number vs. Chromatic Number in Wireless Interference Graphs: Simulation Results
2007
IEEE Communications Letters
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In our extensive simulations with UDGs of random networks, we observed that the clique number and the chromatic number values were typically very close to one another and the maximum deviation was much ...
less than the theoretical bounds. ...
While the chromatic number problem on a UDG is still NP-complete, the clique number problem can be solved in polynomial time in UDGs [3]. ...
doi:10.1109/lcomm.2007.070257
fatcat:vskujgvgnbaeni5kudefbzqhsq
Page 5292 of Mathematical Reviews Vol. , Issue 93j
[page]
1993
Mathematical Reviews
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The bounded chromatic number 7;(G) of G is the smallest number of colors such that G admits a bounded coloring. ...
>n, then the total chromatic number y” < y'+k+1, where
x’ is the edge-chromatic number of G. ...
Page 6613 of Mathematical Reviews Vol. , Issue 99j
[page]
1999
Mathematical Reviews
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(F-PARIS6-CM; Paris)
A bound on the total chromatic number. (English summary) Combinatorica 18 (1998), no. 2, 241-280. ...
The total chromatic number of G is the least number of colours required for a total colouring of G. ...
Chromatic Number and the 2-Rank of a Graph
2001
Journal of combinatorial theory. Series B (Print)
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We show that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2 r +1, and that this bound is tight. ...
Kotlov and Lovasz [6] bound the number of vertices of a reduced graph in terms of the rank, and Kotlov [7] uses this bound to get an improved bound on the chromatic number in terms of the rank. ...
CHROMATIC NUMBER To complete our main result, we merely need to establish the chromatic number of Y(2r). We start by finding a bound on the size of an independent set in Y(2r). ...
doi:10.1006/jctb.2000.2003
fatcat:w2buzib4nbdltl5y2wwgm5bx7q
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