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

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 Edge-colorings avoiding a fixed matching with a prescribed color pattern

2015 ◽  
Vol 47 ◽  
pp. 75-94 ◽  
Author(s):  
Carlos Hoppen ◽  
Hanno Lefmann
Keyword(s):  
Color Pattern ◽  
Edge Colorings

scholarly journals Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces

2015 ◽  
Vol 37 (3) ◽  
pp. 939-970 ◽  
Author(s):  
RUSSELL RICKS
Keyword(s):  
Geodesic Flow ◽  
Isometric Action ◽  
Structural Result ◽  
Curved Manifolds ◽  
Rank One ◽  
Unit Speed ◽  
Flat Strip ◽  
Geodesically Complete ◽  
Positively Curved ◽  
General Technical

Let$X$be a proper, geodesically complete CAT($0$) space under a proper, non-elementary, isometric action by a group$\unicode[STIX]{x1D6E4}$with a rank one element. We construct a generalized Bowen–Margulis measure on the space of unit-speed parametrized geodesics of$X$modulo the$\unicode[STIX]{x1D6E4}$-action. Although the construction of Bowen–Margulis measures for rank one non-positively curved manifolds and for CAT($-1$) spaces is well known, the construction for CAT($0$) spaces hinges on establishing a new structural result of independent interest: almost no geodesic, under the Bowen–Margulis measure, bounds a flat strip of any positive width. We also show that almost every point in$\unicode[STIX]{x2202}_{\infty }X$, under the Patterson–Sullivan measure, is isolated in the Tits metric. (For these results we assume the Bowen–Margulis measure is finite, as it is in the cocompact case.) Finally, we precisely characterize mixing when$X$has full limit set: a finite Bowen–Margulis measure is not mixing under the geodesic flow precisely when$X$is a tree with all edge lengths in$c\mathbb{Z}$for some$c>0$. This characterization is new, even in the setting of CAT($-1$) spaces. More general (technical) versions of these results are also stated in the paper.

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 Extending edge‐colorings of complete hypergraphs into regular colorings

2018 ◽  
Vol 90 (4) ◽  
pp. 547-560 ◽  
Author(s):  
Amin Bahmanian
Keyword(s):  
Edge Colorings

Edge Colorings

2015 ◽  
pp. 465-492
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.

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