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A Bound on the Total Chromatic Number

Michael Molloy, Bruce Reed
1998 Combinatorica  
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

Abdón Sánchez-Arroyo
1995 Discrete Mathematics  
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

R Nisviasari, Dafik, T K Maryati, I H Agustin, E Y Kurniawati
2019 IOP Conference Series: Earth and Environment  
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  
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  
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

Carsten Thomassen, Paul Erdös, Yousef Alavi, Paresh J. Malde, Allen J. Schwenk
1989 Journal of Graph Theory  
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

Stéphane Bessy, Daniel Gonçalves, Jean-Sébastien Sereni
2015 Journal of Graph Algorithms and Applications  
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]

A. Vijayalekshmi
2012 Zenodo  
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  
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  
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]

Stéphane Bessy and Daniel Gonçalves and Jean-Sébastien Sereni
2014 arXiv   pre-print
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

Pradeepkumar Mani, David Petr
2007 IEEE Communications Letters  
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  
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  
(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

C.D. Godsil, Gordon F. Royle
2001 Journal of combinatorial theory. Series B (Print)  
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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