Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Induced Saturation Number   In this paper, we discuss a generalization of the notion of saturation in
graphs in order to deal with induced structures. In particular, we define ${\rm
indsat}(n,H)$, which is the fewest number of gray edges in a trigraph so that
no realization of that trigraph has an induced copy of $H$, but changing any
white or black edge to gray results in some realization that does have an
induced copy of $H$.
  We give some general and basic results and then prove that ${\rm
indsat}(n,P_4)=\lceil (n+1)/3\rceil$ for $n\geq 4$ where $P_4$ is the path on 4
vertices. We also show how induced saturation in this setting extends to a
natural notion of saturation in the context of general Boolean formulas.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
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The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org