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Results tagged with graph-theory
Search options questions only
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user 12481
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.
16
votes
1
answer
696
views
A counterexample to a conjecture of Nash-Williams about hamiltonicity of digraphs?
Maybe I am missing something, but found potential counterexample to a conjecture
of Nash-Williams.
According to HAMILTONIAN DEGREE SEQUENCES IN DIGRAPHS
The outdegree and indegree sequences of digr …
- 25.4k
15
votes
1
answer
1k
views
Is deciding if one planar graph is dual to another really NP-hard (Wikipedia claim)?
Wikipedia claims (permanent link) without reference:
Testing whether one planar graph is dual to another is NP-complete.
Another claim with reference:
For any plane graph G, the medial graph …
- 25.4k
10
votes
2
answers
2k
views
When are the adjacency matrices of non-isomorphic graphs similar?
From Wikipedia.
In linear algebra, two n-by-n matrices A and B are called similar if
$$ B = P^{-1} A P$$
for some invertible n-by-n matrix $P$.
If $P$ is a permutation matrix, $A$ and $B$ are per …
- 25.4k
8
votes
0
answers
199
views
What is the probability of interpolating the Tutte polynomial of a planar graph from the val...
The Tutte polynomial
is a bivariate polynomial with positive integer coefficient which is a graph
invariant and can be defined recursively.
Evaluating it is $\#P$-complete even when restricted to (bip …
- 25.4k
7
votes
1
answer
480
views
Seeming contradiction about P vs NP between graphclasses.org and at least two papers about c...
I believe correctness about clique in even-hole-free graphs
of graphclasses.org
and the paper Vertex elimination orderings for hereditary graph classes, Pierre Aboulker, Pierre Charbit, Nicolas Trotig …
- 25.4k
7
votes
2
answers
440
views
Conjecture: for perfect graphs the fractional chromatic index rounded up equals the chromati...
Let $\chi'_f(G)$ be the fractional chromatic index.
Based on limited experiments (up to 8 vertices and few larger graphs),
I suspect:
Conjecture For perfect graphs $\lceil \chi'_f(G) \rceil = \chi'( …
- 25.4k
7
votes
0
answers
118
views
Contradicting claims about complexity of directed path graphs isomorphism
Thesis and a paper give conflicting claims about the
complexity of graph isomorphism for directed path graphs.
Since this means GI is polynomial likely I am missing something
or there is something el …
- 25.4k
6
votes
0
answers
154
views
Complexity of finding three perfect matchings with no edge in common in a bridgeless cubic g...
According to a conjecture:
Conjecture (Fan & Raspaud, 1994) Every bridgeless cubic graph contains three perfect matchings with no edge in common.
Equivalent statement here
Main question:
Gi …
- 25.4k
6
votes
2
answers
458
views
Is this a counterexample to a conjecture about independent domination in cartesian graph pro...
VIZING’S CONJECTURE: A SURVEY AND RECENT RESULTS (2009) by Bostjan Bresar , Paul Dorbec , Wayne Goddard , Bert L. Hartnell , Michael A. Henning , Sandi Klavzar , Douglas F. Rall
p.25:
Conjectu …
- 25.4k
5
votes
1
answer
218
views
Complexity of counting MAXCUT in planar graphs -- seemingly contradicting claims
Confusion is likely. Appears to me two papers give contradicting claims
about the complexity of counting MAXCUT in planar graphs.
Exact Max 2-SAT: Easier and Faster p. 6
However, counting the num …
- 25.4k
5
votes
1
answer
307
views
Complexity of graph 3 coloring and counting algorithm
3-coloring a graph $G$ is equivalent to partitioning the
vertices of $G$ in three independent sets.
The smallest independent set $A$ is at most $n/3$ where $n$
is the order of $G$.
We have $G \setmi …
- 25.4k
5
votes
0
answers
93
views
Graph gadget related to uniquely hamiltionian regular graphs
A graph is uniquely hamiltonian if it has exactly one hamiltonian cycle.
According to a conjecture there are no $r$-regular uniquely hamiltonian
graphs for $r > 2$ and of special interest is the case …
- 25.4k
5
votes
2
answers
521
views
Diffie Hellman cryptography based on graph isomorphism?
We got a cryptographic algorithm and computer implementation
based on graph isomorphism.
An isomorphism between two graphs is a bijection between their vertices that pre
serves the edges.
For a graph …
- 25.4k
5
votes
1
answer
277
views
Infinitely many counterexamples to Nash-Williams's conjecture about hamiltonicity?
Question from 2013
gives one counterexample to Nash-Williams's conjecture about hamiltonicity
of dense digraphs.
Later, we found tens of counterexamples on more than 30 vertices
and believe there are …
- 25.4k
4
votes
0
answers
105
views
Existence of certain graph gadget related to coloring odd hole free graph
Wondering about the existence of graph gadget related to coloring
(or 3-coloring) odd hole free graphs.
Let $G$ be simple $k$-chromatic connected graph with two
vertices $u,v$.
Is it possible $G$ to …
- 25.4k