Is 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...
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 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 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 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 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 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...
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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...
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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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