# Questions tagged [combinatorial-topology]

The combinatorial-topology tag has no usage guidance.

**4**

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**1**answer

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### Understanding proof about chromatic number

Consider an undirected graph $K(n,k,i)$, with the all $k$-element subsets of $\{1,\dots,n\}$ as vertices, and two vertices connected by an edge if their sets intersect in less than $i$ elements.
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**7**

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**1**answer

326 views

### Kneser graph with overlap

Consider a graph with the vertices being all subsets of size $n$ of a set of size $2n$. Two vertices are connected if their overlap has size at most one. What is the chromatic number of this graph?
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**7**

votes

**1**answer

193 views

### Uniqueness theorem for conformal maping

Let $f$ and $g$ be analytic functions in the unit disk $D$, continuous in the closed disk and locally univalent, $f'(z)\neq 0,\; g'(z)\neq 0,\; z\in D$.
Assume that each has only finitely many ...

**0**

votes

**0**answers

105 views

### Number of polyhedra with N faces?

A. Up to isomorphism, how many polyhedra with N faces are there? Assume each face can be a triangle, square, pentagon, hexagon, etc... Furthermore each edge can be resized to any nonzero positive ...

**6**

votes

**1**answer

170 views

### Existence of a particular kind of polygonal subdivisions of surfaces

Let $\Sigma$ be a closed, compact, connected, oriented smooth $2$-manifold (in other words, a sphere or a torus with $g$ handles). We may draw smooth arcs on the surface in such a way that they cut it ...

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**0**answers

100 views

### Criteria to decide whether a subset of the boundary complex of a polyhedron is a manifold?

Let $\mathcal{P} \subseteq \mathbb{R}^d$ be a convex polyhedron. Let $K$ be a subset of the boundary complex of $\mathcal{P}$. (Perhaps $K$ could be defined in terms of a system of linear inequalities....

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vote

**1**answer

83 views

### property R_\lambda

A space X has property $R_\lambda$ if every family of its clopen sets of cardinality $\lambda$ has a subfamily of cardinality $\lambda$ which is either linked or disjoint.
The following result was ...

**9**

votes

**3**answers

690 views

### Combinatorial distance between simplicial complexes

Let $K_1$ and $K_2$ be two simplicial complexes.
I am seeking a measure of the distance between $K_1$ and $K_2$ when
viewed as combinatorial objects.
What I have in mind is something like this.
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**21**

votes

**4**answers

2k views

### Testing simplicial complexes for shellability

Question
Are there efficient algorithms to check if a finite simplicial complex defined in terms of its maximal facets is shellable?
By efficient here I am willing to consider anything with ...

**23**

votes

**0**answers

2k views

### Are there lots of integer homology three-spheres?

The problem of counting combinatorial three-spheres with $N$ simplices has implications for some partition functions in physics (see a paper by Benedetti and Ziegler for more background and references)...