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I want modify the following example to obtain a colored sub-table (only the border) as in the present picture.

documentclass{article}

usepackage{array}





begin{document}



begin{tabular}{|c|c|c|c|c|}

hline

1 & 3 & 2& B&  C \

hline

A & B&  C& B&  C \

hline

D & E & K& B&  F \

hline

G & H & I& B&  C\

hline

end{tabular}





 end{document}

Not that elegant, but you could use a combination of cline and multicolumn to achieve the desired red frame around the four cells:

documentclass{article}

usepackage{array}

usepackage[table]{xcolor}



begin{document}



begin{tabular}{|c|c|c|c|c|}

hline

1 & 3 & 2& B&  C \

cline{1-2} arrayrulecolor{red}cline{3-4} arrayrulecolor{black}cline{5-5}

A & multicolumn{1}{c!{color{red}vrule}}{B}& C& multicolumn{1}{c!{color{red}vrule}}{B}&  C \

hline

D & multicolumn{1}{c!{color{red}vrule}}{E} & K& multicolumn{1}{c!{color{red}vrule}}{B}&  F \

cline{1-2} arrayrulecolor{red}cline{3-4} arrayrulecolor{black}cline{5-5}

G & H & I& B&  C\

hline

end{tabular}



end{document}

That's just for fun: you can draw pretty much anything with tikz, so why not here? In particular, when using tikzmark you can conveniently annotate whatever you already have.

documentclass{article}

usepackage{array}

usepackage{tikz}

usetikzlibrary{tikzmark,calc}

begin{document}



begin{tabular}{|c|c|c|c|c|}

hline

1 & tikzmarknode{3}{3} & 2& B&  C \

hline

A & B&  tikzmarknode{C1}{C}& B&  C \

hline

D & E & K& tikzmarknode{B}{B}&  F \

hline

G & H & I& B&  tikzmarknode{C2}{C}\

hline

end{tabular}

begin{tikzpicture}[overlay,remember picture]

draw[red,thick] ([yshift=-1pt]$(3)!0.5!(C1)$) rectangle ([yshift=-1pt]$(B)!0.5!(C2)$);

end{tikzpicture}

end{document}

To be clear, I am not suggesting to use this if you only want to draw some red lines. In this case, I think that Leandris' very nice answer is the way to go. However, at the very moment you are interested in more fancy things, then this here might be the way to go.

documentclass{article}

usepackage{array}

usepackage{tikz}

usetikzlibrary{tikzmark,calc}

begin{document}



begin{tabular}{|c|c|c|c|c|}

hline

1 & tikzmarknode{3}{3} & 2& B&  C \

hline

A & B&  tikzmarknode{C1}{C}& B&  C \

hline

D & E & K& tikzmarknode{B}{B}&  F \

hline

G & H & I& B&  tikzmarknode{C2}{C}\

hline

end{tabular}

begin{tikzpicture}[overlay,remember picture]

newlength{Border}

Border=0.8pt

fill[left color=red,right color=blue,shading angle=45,even odd rule] 

([yshift={-1pt+0.5Border},xshift={-0.5Border}]$(3)!0.5!(C1)$) rectangle 

([yshift={-1-0.5Border},xshift={+0.5Border}]$(B)!0.5!(C2)$)

[rounded corners]

([yshift={-1pt-0.5Border},xshift={0.5Border}]$(3)!0.5!(C1)$) rectangle 

([yshift={-1pt+0.5Border},xshift={-0.5Border}]$(B)!0.5!(C2)$)

;

end{tikzpicture}

end{document}

You can use cellcolor{..} to color single cells. You need the xcolor package or just the colortbl package, the former loads the latter. Note that some PDF viewers hide table lines behind the color.

documentclass{article}

usepackage{array}

usepackage[table]{xcolor}



begin{document}



begin{tabular}{|c|c|c|c|c|}

hline

1 & 3 & 2& B&  C \hline

A & B&  cellcolor{blue!25}C& cellcolor{blue!25}B&  C \hline

D & E & cellcolor{blue!25}K& cellcolor{blue!25}B&  F \hline

G & H & I& B&  C \hline

end{tabular}



end{document}