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ProblemCourse & topicStatus

DM:9919259Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919260Let H be a 3-uniform hypergraph with n vertices and m edges.

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919261Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919262Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919263Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919264Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919265Let G be a simple graph on 2n vertices in which every vertex has degree at least n.

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919266Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919267Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919268Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919269Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919270Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919271Let n $\ge$ 2.

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919272Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919273Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919274Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919275Let P be a finite poset.

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919276Let J(P) be the lattice of order ideals of a finite poset P, ordered by inclusion.

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919277Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919278Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919279Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919280Let A be a finite Boolean algebra with 16 elements.

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

—

DM:9919281Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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DM:9919282Mathematical problem title

GraphsDiscrete Mathematics Problem Solving

Graphs, trees, connectivity, and matchingsDiscrete Mathematics · Mixed review

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Showing 24 of 42 matching problems.

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Prove that if

\binom{n}{k}\bigl(1-2^{-k}\bigr)^{n-k}<1

, then there exists a tournament on n vertices in which…

Let G be a simple graph of maximum degree

\Delta

.

Viewing subsets of [n] as vertices of the n-dimensional hypercube, prove that every family

\mathcal{F}

of more…

Let

A_1,\dots,A_m\subseteq[n]

with

\lvert

A_i\rvert=k\ge

1 for each i.

Let G be the graph obtained from the complete bipartite graph

K_{3,3}

by subdividing every edge exactly once, and…

A matching M in a graph G is maximal if no strictly larger matching contains M, and maximum if

\lvert

M\rvert

is…

Let G be a simple n-vertex graph containing no

K_r

as a subgraph, where r

\ge

3 is fixed.

Let G be a simple graph with vertex set

\{1

, 2,

\ldots

,

8\}

in which ij is an edge if and only if

\lvert

i…

The Ramsey number R(3, 4) is the smallest N such that every 2-edge-coloring of

K_N

contains a red

K_3

or a blue

K_4

.

Let G be the Cartesian product

C_5

\square

K_2

(the pentagonal prism).

Let P be the poset of all subsets of

\{1

, 2, 3,

4\}

of cardinality 2, ordered by inclusion (so incomparable 2-sets…

Let

B_n

be the Boolean lattice of subsets of [n] =

\{1

, 2,

\ldots

,

n\}

ordered by inclusion.

A finite lattice L is distributive if a

\wedge

(b

\vee

c) = (a

\wedge

b)

\vee

(a

\wedge

c) for all a, b, c

\in

L.

Let f :

\{0,1\}^4

\to

\{0,1\}

be the Boolean function that equals 1 if and only if at least three of the four…

For a Boolean function g :

\{0,1\}^n

\to

\{0,1\}

, the dual is

g^d(x)

= 1 - g(1 -

x_1

,

\ldots

, 1 -

x_n)

.

A Boolean function f is monotone if x

\le

y componentwise implies f(x)

\le

f(y).

The Reed–Muller expansion of a Boolean function f :

\{0,1\}^n

\to

\{0,1\}

is the unique multilinear polynomial…

Let P be a finite poset and let

G_P

be the comparability graph of P (vertices are elements of P, edges join…