Random Walks and Forbidden Minors I: An $n^{1/2+o(1)}$-Query One-Sided Tester for Minor Closed Properties on Bounded Degree Graphs

2020 ◽  
pp. FOCS18-216-FOCS18-249
Author(s):  
Akash Kumar ◽  
C. Seshadhri ◽  
Andrew Stolman
Keyword(s):  
Random Walks ◽  
Bounded Degree ◽  
Bounded Degree Graphs ◽  
Forbidden Minors

scholarly journals A short note on conflict‐free coloring on closed neighborhoods of bounded degree graphs

2021 ◽  
Author(s):  
Sriram Bhyravarapu ◽  
Subrahmanyam Kalyanasundaram ◽  
Rogers Mathew
Keyword(s):  
Short Note ◽  
Bounded Degree ◽  
Bounded Degree Graphs

scholarly journals EMBEDDING SPANNING BOUNDED DEGREE GRAPHS IN RANDOMLY PERTURBED GRAPHS

Mathematika ◽  
2020 ◽  
Vol 66 (2) ◽  
pp. 422-447 ◽  
Author(s):  
Julia Böttcher ◽  
Richard Montgomery ◽  
Olaf Parczyk ◽  
Yury Person
Keyword(s):  
Bounded Degree ◽  
Bounded Degree Graphs

Very rapid mixing of the Glauber dynamics for proper colorings on bounded-degree graphs

2002 ◽  
Vol 20 (1) ◽  
pp. 98-114 ◽  
Author(s):  
Martin Dyer ◽  
Catherine Greenhill ◽  
Mike Molloy
Keyword(s):  
Glauber Dynamics ◽  
Bounded Degree ◽  
Rapid Mixing ◽  
Bounded Degree Graphs

scholarly journals Optimal induced universal graphs for bounded-degree graphs

2017 ◽  
Vol 166 (1) ◽  
pp. 61-74 ◽  
Author(s):  
NOGA ALON ◽  
RAJKO NENADOV
Keyword(s):  
Maximum Degree ◽  
Constant Factor ◽  
Induced Subgraph ◽  
Bounded Degree ◽  
Vertex Graph ◽  
Bounded Degree Graphs ◽  
Universal Graphs

AbstractWe show that for any constant Δ ≥ 2, there exists a graph Γ withO(nΔ / 2) vertices which contains everyn-vertex graph with maximum degree Δ as an induced subgraph. For odd Δ this significantly improves the best-known earlier bound and is optimal up to a constant factor, as it is known that any such graph must have at least Ω(nΔ/2) vertices.

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