List questions from extremal-combinatorics

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Trimming down a relation to a partial order

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Un-monochromatic Arithmetic Progressions

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Prove that the points can be covered by a heptagon of area $\dfrac{10}{3}$

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Ramsey Theory Similar Problem

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Combinatorial viewpoint regarding n Points and collinearity

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Proving that if a sequence of integers satisfies $0<a_{k+1}-a_k<r$, then it contains arbitrarily long arithmetic progressions

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Largest subset with no arithmetic progresssions

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The Sums of the Subsets are Distinct

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Unsolved Perfect Coverings

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Minimum number of vertices covered by any 1/3 of edges in a graph

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Proof that there does not exist a regular intersecting family of subsets of an $n$-set having size $2^{n-1}$ if $n$ is a power of $2$.

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Finite limit to size of Intersecting Family with no Smaller Intersecting Set?

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Optimizing a network of multi-pole switches

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Number of rounds for a tournament with n teams and $x$ types of games

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List Question

Maximum area of triangle inside a convex polygon

Trimming down a relation to a partial order

Un-monochromatic Arithmetic Progressions

Prove that the points can be covered by a heptagon of area $\dfrac{10}{3}$

Ramsey Theory Similar Problem

Combinatorial viewpoint regarding n Points and collinearity

Proving that if a sequence of integers satisfies $0<a_{k+1}-a_k<r$, then it contains arbitrarily long arithmetic progressions

Largest subset with no arithmetic progresssions

The Sums of the Subsets are Distinct

Unsolved Perfect Coverings

Minimum number of vertices covered by any 1/3 of edges in a graph

Proof that there does not exist a regular intersecting family of subsets of an $n$-set having size $2^{n-1}$ if $n$ is a power of $2$.

Finite limit to size of Intersecting Family with no Smaller Intersecting Set?

Optimizing a network of multi-pole switches

Number of rounds for a tournament with n teams and $x$ types of games

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