Cliques, Chromatic Number, and Independent Sets in the Semi-random Process

Gamarnik, David; Kang, Mihyun; Prałat, Paweł

doi:10.1137/23m1561105

SIAM J. Discrete Math.

2024

DOI: 10.1137/23m1561105

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Cliques, Chromatic Number, and Independent Sets in the Semi-random Process

David Gamarnik,

Mihyun Kang,

Paweł Prałat

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2024

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Cited by 1 publication

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On the Pre‐ and Post‐Positional Semi‐Random Graph Processes

Gao,

Koerts

2024

Journal of Graph Theory

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We study the semi‐random graph process, and a variant process recently suggested by Nick Wormald. We show that these two processes are asymptotically equally fast in constructing a semi‐random graph that has property , for the following examples of : (1) is the set of graphs containing a fixed ‐degenerate subgraph, where is fixed and (2) is the set of ‐connected graphs, where is fixed. In particular, our result of the ‐connectedness above settles the open case of the original semi‐random graph process. We also prove that there exist properties where the two semi‐random graph processes do not construct a graph in asymptotically equally fast. We further propose some conjectures on for which the two processes perform differently.

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On the Pre‐ and Post‐Positional Semi‐Random Graph Processes

Gao,

Koerts

2024

Journal of Graph Theory

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show abstract

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Cliques, Chromatic Number, and Independent Sets in the Semi-random Process

Cited by 1 publication

References 13 publications

On the Pre‐ and Post‐Positional Semi‐Random Graph Processes

On the Pre‐ and Post‐Positional Semi‐Random Graph Processes

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