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Results tagged with graph-theory
Search options questions only
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user 1946
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
31
votes
3
answers
2k
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Is the Rado graph a Cayley graph? If so, what is the group like? (And other questions...)
The countable random graph, also known as the Rado graph, is characterized as the unique countable graph in which every two disjoint finite sets $A$ and $B$ of vertices admit a vertex $p$ connected to …
- 236k
19
votes
2
answers
985
views
Which graphs are elementarily equivalent to their own disjoint sums?
In Stefan Geschke's recent
question,
one of the solutions observed that the graph consisting of
a single infinite beaded chain, a $\mathbb{Z}$-chain where
each integer is connected to its nearest neig …
- 236k
9
votes
2
answers
496
views
Can a parent and child node have the same type in a well-founded digraph tree?
$\newcommand\toward{\rightharpoonup}$It would help me to
understand something in a current research project if someone
could provide an example of directed graph $\langle
G,\toward\rangle$ with the fo …
- 236k
47
votes
7
answers
5k
views
Is it easy to produce hard-to-color graphs?
This question arises from my recent visit to my daughter's second-grade class, where I led some discussion and activities on graph coloring (see Math for seven-year-olds). In one such activity, each c …
- 236k
32
votes
9
answers
5k
views
How many groups of size at most n are there? What is the asymptotic growth rate? And what of...
Question. How many (isomorphism types of) finite groups of size at most n are there? What is the asymptotic growth rate? And the same question for rings,
fields, graphs, partial orders, etc.
Motiva …
- 236k
76
votes
6
answers
9k
views
Which graphs are Cayley graphs?
Every group presentation determines the corresponding Cayley graph, which has a node for each group element, and arrows labeled with the generators to get from one group element to another.
My main …
- 236k