scholarly journals The edge colorings of K5-minor free graphs

2021 ◽  
Vol 344 (6) ◽  
pp. 112360
Author(s):  
Jieru Feng ◽  
Yuping Gao ◽  
Jianliang Wu
Keyword(s):  
Edge Colorings ◽  
Minor Free Graphs

scholarly journals Reflexive coloring complexes for 3-edge-colorings of cubic graphs

2021 ◽  
Vol 344 (4) ◽  
pp. 112309
Author(s):  
Fiachra Knox ◽  
Bojan Mohar ◽  
Nathan Singer
Keyword(s):  
Cubic Graphs ◽  
Edge Colorings

scholarly journals A note on upper bounds for the maximum span in interval edge-colorings of graphs

2012 ◽  
Vol 312 (8) ◽  
pp. 1393-1399 ◽  
Author(s):  
R.R. Kamalian ◽  
P.A. Petrosyan
Keyword(s):  
Upper Bounds ◽  
Edge Colorings ◽  
Maximum Span

scholarly journals Orientable edge colorings of graphs

2011 ◽  
Vol 159 (7) ◽  
pp. 595-604
Author(s):  
Robert E. Jamison
Keyword(s):  
Edge Colorings

scholarly journals On the Ramsey Number $R(4,6)$

10.37236/2102 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Fixed Point ◽  
Automorphism Group ◽  
Lower Bound ◽  
Heuristic Search ◽  
Ramsey Number ◽  
Complete Graphs ◽  
Search Procedure ◽  
Edge Colorings

The lower bound for the classical Ramsey number $R(4,6)$ is improved from 35 to 36. The author has found 37 new edge colorings of $K_{35}$ that have no complete graphs of order 4 in the first color, and no complete graphs of order 6 in the second color. The most symmetric of the colorings has an automorphism group of order 4, with one fixed point, and is presented in detail. The colorings were found using a heuristic search procedure.

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