Constrained outer-string representations for {C3,C5}-free graphs are polynomial-time recognizable by forbidden configuration; outer-k-string recognition is NP-hard for every fixed k >= 1.
Recognizing string graphs in
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Two Results on Outer-String Graphs
Constrained outer-string representations for {C3,C5}-free graphs are polynomial-time recognizable by forbidden configuration; outer-k-string recognition is NP-hard for every fixed k >= 1.