scholarly journals Notes on weak-odd edge colorings of digraphs

2021 ◽  
Author(s):  
César Hernández-Cruz ◽  
Mirko Petruševski ◽  
Riste Škrekovski
Keyword(s):  
Edge Colorings

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.

scholarly journals A note on compact and compact circular edge-colorings of graphs

2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Dariusz Dereniowski ◽  
Adam Nadolski
Keyword(s):  
Approximation Algorithm ◽  
Decision Problem ◽  
Edge Coloring ◽  
Exact Algorithm ◽  
Weighted Graphs ◽  
Edge Colorings ◽  
Odd Cycle ◽  
International Audience ◽  
Np Complete ◽  
Odd Cycles

Graphs and Algorithms International audience We study two variants of edge-coloring of edge-weighted graphs, namely compact edge-coloring and circular compact edge-coloring. First, we discuss relations between these two coloring models. We prove that every outerplanar bipartite graph admits a compact edge-coloring and that the decision problem of the existence of compact circular edge-coloring is NP-complete in general. Then we provide a polynomial time 1:5-approximation algorithm and pseudo-polynomial exact algorithm for compact circular coloring of odd cycles and prove that it is NP-hard to optimally color these graphs. Finally, we prove that if a path P2 is joined by an edge to an odd cycle then the problem of the existence of a compact circular coloring becomes NP-complete.

scholarly journals Sum list edge colorings of graphs

2016 ◽  
Vol 36 (3) ◽  
pp. 709 ◽  
Author(s):  
Arnfried Kemnitz ◽  
Massimiliano Marangio ◽  
Margrit Voigt
Keyword(s):  
Edge Colorings

scholarly journals A structural result for hypergraphs with many restricted edge colorings

2010 ◽  
Vol 1 (4) ◽  
pp. 441-475 ◽  
Author(s):  
Hanno Lefmann ◽  
Yury Person ◽  
Mathias Schacht
Keyword(s):  
Structural Result ◽  
Edge Colorings
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