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Weird claim of graphclasses about complexity of domination
EDIT this got ‘fixed’ on graphclasses, as per answers/comments, so you might not reproduce it, unless you have their earlier database, which is publicly available via sage – http://sagemath.org. Likely...
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Name the graph class: Disjoint union of a clique and an independent set
Let $G$ be a graph which is the disjoint union of a clique and an independent set, i.e. $$G = K_{n_1} + overline{K_{n_2}} = K_{n_1} + I_{n_2} .$$ The graph class of all such graphs is characterized by...
View ArticleCan a natural graph problem be universally hard?
Is there a natural $mathsf{NP}$-complete graph problem, which remains $mathsf{NP}$-complete even when it is restricted to any polynomial-time recognizable graph class? To avoid degenerated cases, let...
View ArticleNatural graph class with five excluded subgraphs?
I’m interested in hereditary graph classes characterized by a small number of excluded subgraphs. There are some well-known graph classes that are characterized by three or four obstructions — examples...
View ArticleIs it necessary to call matrix multiplication $n$ times to find a claw
A claw is a $K_{1,3}$. A trivial algorithm will detect a claw in $O(n^4)$ time. It can be done in $O(n^{omega+1})$, where $omega$ is the exponent of fast matrix multiplication, as follows: take the...
View ArticleEdge Cut of interval graphs
On interval graphs, minimal vertex separators are well understood: they are cliques, there are no more than $n$ ones. However, when we turn to the minimal edge cut, my search found no even one single...
View ArticleIs there any triangle-free, star-cutset-free, circle graph, with more than n...
I’m trying to find a graph with those properties for my studies, but unfortunately I can’t find such graph. Does anyone know if there is that graph, or why is it impossible to exist?
View ArticleDoes this graph class have a name ?
It’s formulated by extending threshold graphs. Given a threshold graph $(C,I)$ where $C$ is the clique and $I$ is the independent set, my extension is as follows: Each vertex $vin I$ can be replaced by...
View ArticleIs any chordal graph an incomparability graph?
I was confused by Wikipedia’s definitions of “chordal graph“, “interval graph“, “string graph“, “comparability graph“, “incomparability graph” and the complements of these. Wikipedia says “The...
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