Some upper bounds for the total chromatic number of graphs

1996 ◽  
pp. 104-113
Author(s):  
Hian-Poh Yap
Keyword(s):  
Chromatic Number ◽  
Upper Bounds ◽  
Total Chromatic Number

scholarly journals Total chromatic number of one kind of join graphs

2006 ◽  
Vol 306 (16) ◽  
pp. 1895-1905 ◽  
Author(s):  
Guangrong Li ◽  
Limin Zhang
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number

A Unique Approach on Upper Bounds for the Chromatic Number of Total Graphs

2012 ◽  
Vol 5 (4) ◽  
pp. 240-246
Author(s):  
J. Venkateswara Rao ◽  
R.V.N. Srinivasa Rao
Keyword(s):  
Chromatic Number ◽  
Upper Bounds ◽  
Unique Approach

A Characterization of Graphs with Fractional Total Chromatic Number Equal to

2009 ◽  
Vol 35 ◽  
pp. 235-240 ◽  
Author(s):  
Takehiro Ito ◽  
W. Sean Kennedy ◽  
Bruce A. Reed
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number

scholarly journals Total Coloring Conjecture for Certain Classes of Graphs

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 161 ◽  
Author(s):  
R. Vignesh ◽  
J. Geetha ◽  
K. Somasundaram
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Line Graph ◽  
Product Line ◽  
Total Coloring ◽  
Lexicographic Product ◽  
Total Chromatic Number ◽  
Minimum Number ◽  
Total Coloring Conjecture

A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by χ ′ ′ ( G ) , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, Δ ( G ) + 1 ≤ χ ′ ′ ( G ) ≤ Δ ( G ) + 2 , where Δ ( G ) is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph.

Coloring squares of graphs via vertex orderings

2020 ◽  
pp. 2050093
Author(s):  
Mehmet Akif Yetim
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Chordal Graph ◽  
Upper Bounds ◽  
Cocomparability Graph ◽  
Vertex Ordering

We provide upper bounds on the chromatic number of the square of graphs, which have vertex ordering characterizations. We prove that [Formula: see text] is [Formula: see text]-colorable when [Formula: see text] is a cocomparability graph, [Formula: see text]-colorable when [Formula: see text] is a strongly orderable graph and [Formula: see text]-colorable when [Formula: see text] is a dually chordal graph, where [Formula: see text] is the maximum degree and [Formula: see text] = max[Formula: see text] is the multiplicity of the graph [Formula: see text]. This improves the currently known upper bounds on the chromatic number of squares of graphs from these classes.

scholarly journals AVD-total-chromatic number of some families of graphs with Δ(G)=3

2017 ◽  
Vol 217 ◽  
pp. 628-638 ◽  
Author(s):  
Atílio G. Luiz ◽  
C.N. Campos ◽  
C.P. de Mello
Keyword(s):  
Chromatic Number ◽  
Total Chromatic Number
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