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Results tagged with graph-theory
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user 6322
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.
1
vote
Deciding whether a given graph has an f-factor or not!
Yes; in fact, one can find in polynomial time a subgraph that is "as close as possible" to being an $f$-factor, if no $f$-factor exists. See, for example, Hell-Kirkpatrick: http://www.sciencedirect.co …
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8
votes
Accepted
How many uniquely colored degree two vertices in 3-coloring of subcubic graph?
No such graph exists (that is, you cannot have a subcubic graph with three degree-$2$ vertices all forced to the same color). Suppose that such a graph exists; we may assume the graph is connected. Th …
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9
votes
Accepted
What is the correct statement of this Erdös-Gallai-Tuza problem generalizing Turan's triangl...
I hope I am not violating any kind of MathOverflow etiquette by responding to a question 2 years after it has been asked, but your question is answered in the following preprint of mine that just hit …
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6
votes
Proving Hall's marriage theorem using Sperner's lemma
In addition to Carlo Beenakker's answer that gives Hall via Sperner directly, I think you can also get it by applying Hall's Theorem for Hypergraphs as follows. Let $G$ be a bipartite graph with parti …
- 681
5
votes
Accepted
List chromatic index of a particular graph
Greedy coloring works here to show $2p$-choosability, I believe, and the hypothesis that $p$ is prime doesn't appear to be necessary. Write the cliques as $A = \{a_1, \ldots, a_{p+1}\}$ and $B = \{b_1 …
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12
votes
Accepted
Blinking graphs
This question seems quite similar to the problem of parity domination. Let $S$ be the set of vertices with label $1$. The condition that $S$ flips to its complement after updating is equivalent to the …
- 681