Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 148974

Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

4 votes
0 answers
129 views

What is the crossing number of dodecahedron with a copy of $K_5$ inside each face

Suppose we are given a regular dodecahedron. Then we add five crossed edges inside each of its faces (actually, inside each face it is a copy of $K_5$). It is clear that this drawing has 60 crossings. …
Xin Zhang's user avatar
  • 1,190
3 votes
1 answer
196 views

Looking for examples showing that the crossing number may not be realized by the drawings wi...

The crossing number $cr(G)$ of a graph $G$ is the lowest number of edge crossings of a plane drawing of the graph $G$. The local crossing number of a drawing of a graph is the largest number of crossi …
Xin Zhang's user avatar
  • 1,190
6 votes
2 answers
289 views

Is there any maximal 1-planar or 2-planar graph that is not 3-connected

A graph is $k$-planar if it can be drawn in the plane so that each edge is crossed at most $k$ times. A $k$-planar graph $G$ is maximal if $G+uv$ is not $k$-planar for any non-adjacent vertices $u,v\i …
Xin Zhang's user avatar
  • 1,190
5 votes
1 answer
260 views

What is the crossing number of cube with a pair of crossing edges inside each face

Suppose we are given a cube and we add a pair of crossing edges inside each of its faces. It is clear that this drawing has 6 crossings. My question is whether such a graph has crossing number 6? How …
Xin Zhang's user avatar
  • 1,190
6 votes
1 answer
286 views

Generating 21-vertex 4-regular plane graphs with 8 faces of degree 3 and 15 faces of degree 4

Is there any way to generate all 4-regular plane graphs with 21 vertices, 8 faces of degree 3, and 15 faces of degree 4? If so, how many of these graphs are there and what are they?
Xin Zhang's user avatar
  • 1,190
3 votes
Accepted

Is there any maximal 1-planar or 2-planar graph that is not 3-connected

This is a non-3-connected 1-planar example...
Xin Zhang's user avatar
  • 1,190
7 votes
2 answers
251 views

There is a 3-connected 5-regular simple $n$-vertex planar graph iff $n$ satisfies....?

Is there any characterization on the set of integers $n$ such that there is a 3-connected 5-regular simple $n$-vertex planar graph?
Xin Zhang's user avatar
  • 1,190
4 votes

Is it possible that every edge in a 1-planar drawing with minimum number of crossings is cro...

Concerning the above answer, I do not quite agree with the last sentence. Why is there some vertex of $D^\times$ outside $O$ if $y$ is a dummy vertex on $C$? I draw a figure, where $y$ is a dummy vert …
Xin Zhang's user avatar
  • 1,190