Pith. sign in

REVIEW

On resilient hypergraphs

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.08406 v1 pith:WD5R2VST submitted 2025-03-11 math.CO

On resilient hypergraphs

classification math.CO
keywords numbergraphmatchingresilientconjectureverticesarbitrarybounds
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The matching number of a $k$-graph is the maximum number of pairwise disjoint edges in it. The $k$-graph is called $t$-resilient if omitting $t$ vertices never decreases its matching number. The complete $k$-graph on $sk+k-1$ vertices has matching number $s$ and it is easily seen to be $(k-1)$-resilient. We conjecture that this is maximal for $k=3$ and $s$ arbitrary. The main result verifies this conjecture for $s=2$. Then Theorem 1.9 provides a considerable improvement on the known upper bounds for $s\geq 3$.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.