Fractional chromatic number and circular chromatic number for distance graphs with large clique size

2004 ◽  
Vol 47 (2) ◽  
pp. 129-146 ◽  
Author(s):  
Daphne Der-Fen Liu ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Distance Graphs ◽  
Circular Chromatic Number ◽  
Fractional Chromatic Number ◽  
Large Clique

scholarly journals Cubical coloring — fractional covering by cuts and semidefinite programming

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Robert Šámal
Keyword(s):  
Semidefinite Programming ◽  
Chromatic Number ◽  
Fractional Chromatic Number ◽  
Maximum Cut ◽  
Continuous Mappings ◽  
Polynomial Time Approximation Algorithm ◽  
Eigenvalue Bound ◽  
International Audience ◽  
Graph Parameters ◽  
Fractional Covering

International audience We introduce a new graph parameter that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with chromatic number, bipartite density, and other graph parameters. We find the value of our parameter for a family of graphs based on hypercubes. These graphs play for our parameter the role that cliques play for the chromatic number and Kneser graphs for the fractional chromatic number. The fact that the defined parameter attains on these graphs the correct value suggests that our definition is a natural one. In the proof we use the eigenvalue bound for maximum cut and a recent result of Engström, Färnqvist, Jonsson, and Thapper [An approximability-related parameter on graphs – properties and applications, DMTCS vol. 17:1, 2015, 33–66]. We also provide a polynomial time approximation algorithm based on semidefinite programming and in particular on vector chromatic number (defined by Karger, Motwani and Sudan [Approximate graph coloring by semidefinite programming, J. ACM 45 (1998), no. 2, 246–265]).

scholarly journals T-colorings, divisibility and circular chromatic number

2021 ◽  
Vol 41 (2) ◽  
pp. 441
Author(s):  
Robert Janczewski ◽  
Anna Maria Trzaskowska ◽  
Krzysztof Turowski
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number

scholarly journals Circular chromatic number and Mycielski construction

2003 ◽  
Vol 44 (2) ◽  
pp. 106-115 ◽  
Author(s):  
Hossein Hajiabolhassan ◽  
Xuding Zhu
Keyword(s):  
Chromatic Number ◽  
Circular Chromatic Number

Chromatic number of distance graphs generated by the sets {2,3,x,y}

2012 ◽  
Vol 25 (4) ◽  
pp. 680-693 ◽  
Author(s):  
Daphne Der-Fen Liu ◽  
Aileen Sutedja
Keyword(s):  
Chromatic Number ◽  
Distance Graphs
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