scholarly journals Synchronization of a bounded degree graph of cellular automata with nonuniform delays in time D⌊logmD⌋

2006 ◽  
Vol 356 (1-2) ◽  
pp. 170-185 ◽  
Author(s):  
Serge Grigorieff
Keyword(s):  
Cellular Automata ◽  
Bounded Degree ◽  
Degree Graph

scholarly journals Cellular automata over generalized Cayley graphs

2017 ◽  
Vol 28 (3) ◽  
pp. 340-383 ◽  
Author(s):  
PABLO ARRIGHI ◽  
SIMON MARTIEL ◽  
VINCENT NESME
Keyword(s):  
Cellular Automata ◽  
Metric Space ◽  
Cayley Graphs ◽  
Continuous Functions ◽  
Point Of View ◽  
Automata Theory ◽  
Time Varying ◽  
Compact Metric Space ◽  
Bounded Degree ◽  
Translation Invariant

It is well-known that cellular automata can be characterized as the set of translation-invariant continuous functions over a compact metric space; this point of view makes it easy to extend their definition from grids to Cayley graphs. Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to an origin; and the fact that they have a well-defined notion of translation. We propose a notion of graphs, which preserves or generalizes these features. Whereas Cayley graphs are very regular, generalized Cayley graphs are arbitrary, although of a bounded degree. We extend cellular automata theory to these arbitrary, bounded degree, time-varying graphs. The obtained notion of cellular automata is stable under composition and under inversion.

scholarly journals Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of GLn-Complexes

2001 ◽  
Vol 239 (1) ◽  
pp. 77-92 ◽  
Author(s):  
Dikran B. Karaguezian ◽  
Victor Reiner ◽  
Michelle L. Wachs
Keyword(s):  
Bounded Degree ◽  
Graph Complexes ◽  
Degree Graph

scholarly journals Computing the Number of Induced Copies of a Fixed Graph in a Bounded Degree Graph

Algorithmica ◽  
2018 ◽  
Vol 81 (5) ◽  
pp. 1844-1858 ◽  
Author(s):  
Viresh Patel ◽  
Guus Regts
Keyword(s):  
Bounded Degree ◽  
Degree Graph

Bounded degree graph inference from walks

COLT ◽  
1991 ◽  
pp. 354-366
Author(s):  
Vijay Raghavan
Keyword(s):  
Bounded Degree ◽  
Degree Graph ◽  
Graph Inference

scholarly journals Topology of bounded-degree graph complexes

2003 ◽  
Vol 262 (2) ◽  
pp. 287-312 ◽  
Author(s):  
Xun Dong
Keyword(s):  
Bounded Degree ◽  
Graph Complexes ◽  
Degree Graph

scholarly journals KŐNIG’S LINE COLORING AND VIZING’S THEOREMS FOR GRAPHINGS

2016 ◽  
Vol 4 ◽  
Author(s):  
ENDRE CSÓKA ◽  
GÁBOR LIPPNER ◽  
OLEG PIKHURKO
Keyword(s):  
Maximum Degree ◽  
Edge Coloring ◽  
Classical Theorem ◽  
Orbit Equivalence ◽  
Bounded Degree ◽  
Finite Graphs ◽  
Edge Colorings ◽  
Graph Limits ◽  
Degree Graph ◽  
Odd Cycles

The classical theorem of Vizing states that every graph of maximum degree $d$ admits an edge coloring with at most $d+1$ colors. Furthermore, as it was earlier shown by Kőnig, $d$ colors suffice if the graph is bipartite. We investigate the existence of measurable edge colorings for graphings (or measure-preserving graphs). A graphing is an analytic generalization of a bounded-degree graph that appears in various areas, such as sparse graph limits, orbit equivalence and measurable group theory. We show that every graphing of maximum degree $d$ admits a measurable edge coloring with $d+O(\sqrt{d})$ colors; furthermore, if the graphing has no odd cycles, then $d+1$ colors suffice. In fact, if a certain conjecture about finite graphs that strengthens Vizing’s theorem is true, then our method will show that $d+1$ colors are always enough.

scholarly journals Bounded degree graph inference from walks

1994 ◽  
Vol 49 (1) ◽  
pp. 108-132 ◽  
Author(s):  
Vijay Raghavan
Keyword(s):  
Bounded Degree ◽  
Degree Graph ◽  
Graph Inference
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