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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.
2
votes
0
answers
68
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Is this infinite family of non-trivial snarks resulting from the first Celmins-Swart?
Non-trivial snark is cubic graph with chromatic index $4$, girth
at least $5$ and doesn't to contain three edges whose deletion results in a disconnected graph, each of whose components is nontrivial. …
- 25.4k
3
votes
1
answer
103
views
Let $S$ be the nonempty set of strongly regular graphs with given parameters. Must $S$ conta...
As the title says, let $S$ be the nonempty set of strongly regular graphs with given parameters. Must $S$ contain vertex transitive graph?
I suspect the most likely counterexample would be $|S|=1$.
- 25.4k
2
votes
0
answers
124
views
Maximizing the minimum outdegree of digraph without $m$ cycle
Let $G$ be a simple digraph on $n$ vertices without a directed cycle of length $m$
(it may have directed cycles of length less than $m$. The cycles need not be simple).
How large the minimum outde …
- 25.4k
1
vote
0
answers
47
views
Complexity of computing the Tutte polynomial of multigraph when the Tutte polynomial of the ...
Let $G$ be multigraph with $l$ loops and $m$ multiple edges and $G'$ be the
underlying simple graph (loops and multiple edges removed).
Assume the Tutte polynomial of $G'$ is given.
Q1 What is th …
- 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
0
votes
0
answers
154
views
For which matrices deciding permutation similarity is polynomial?
Q1 For which matrices deciding permutation similarity is polynomial?
It is not easier than graph isomorphism (and very likely is equivalent to it).
If necessary, assume the entries are nonnegati …
- 25.4k
2
votes
1
answer
180
views
Graph classes where finding explicit coloring have certificate that it is minumum
Graph coloring doesn't have certificate that smaller coloring doesn't exist in general.
I am looking for graph classes where finding explicit coloring is not polynomial and have polynomially verifiab …
- 25.4k
2
votes
1
answer
259
views
The edge chromatic number and pefectness of inflation of cubic graph
The inflation of graph $G$ is a graph $I(G)$
which is obtained by replacing each vertex $x$ by a complete graph
$K_{\deg(x)}$ and joining each edge to a different vertex of $K_{\deg(x)}$.
Let $G$ b …
- 25.4k
4
votes
1
answer
957
views
Coloring tensor products of graphs
Let $ G,H $ are simple finite graphs and $A = G \times H$. Here $ G \times H $ is the tensor product (also called the direct or categorical product) of $ G $ and $ H $.
Let $G$ has smaller chromatic …
- 25.4k
1
vote
1
answer
98
views
Would a graph with such maximum weighted matchings exist?
Edit Tony's answer is quite nice, but I meant something else. Sorry for editing again, I meant edges.
I am looking for a graph with 3 distinguished edges $xx'$,$yy'$,$zz'$ where $\deg(x)=\deg(y)=\deg …
- 25.4k
2
votes
0
answers
87
views
Complexity consequence of logarithmic boolean width of co-bounded degree graphs?
The paper On graph classes with logarithmic
boolean-width claims that the
boolean width of co-k-degenerate graphs is at most $k\log{n}$
and a lot of graph vertex partition problems can be solved in
po …
- 25.4k
2
votes
0
answers
99
views
Can we efficiently count modulo 2 the number of connected subgraphs of a planar graph?
Paper p.9 and Wikipedia
relate the Tutte polynomial of a graph to another polynomial.
If $(x-1)(y-1)=z$, $$T(G;x,y)=F_G(z,y)/H(G)$$
Where $F_G(z,y)=\sum_{A \subseteq E}z^{c(G_A)}(y-1)^{|A|} $
where …
- 25.4k
1
vote
1
answer
127
views
Reduction graph to planar bounded treewidth graph
We got reduction graph to planar bounded treewidth graph,
but this is unlikely to be true.
Let $H$, the planarizing gadget, be planar graph with four
distinguished vertices $u,u',v,v'$ on the outer f …
- 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
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