Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the Ramsey Number $R(K_5-P_3,K_5)$   We give a computer-assisted proof of the fact that $R(K_5-P_3, K_5)=25$. This
solves one of the three remaining open cases in Hendry's table, which listed
the Ramsey numbers for pairs of graphs on 5 vertices. We find that there exist
no $(K_5-P_3,K_5)$-good graphs containing a $K_4$ on 23 or 24 vertices, where a
graph $F$ is $(G,H)$-good if $F$ does not contain $G$ and the complement of $F$
does not contain $H$. The unique $(K_5-P_3,K_5)$-good graph containing a $K_4$
on 22 vertices is presented.

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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph