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More in “Word-representation of graphs”

• Are there any graphs on n vertices whose representation requires more than floor(n/2) copies of each letter?
• Characterise word-representable graphs in terms of (induced) forbidden subgraphs.
• Characterise word-representable near-triangulations containing the complete graph K4 (such a characterisation is known for K4-free planar…
• Classify graphs with representation number 3, that is, graphs that can be represented using 3 copies of each letter, but cannot be…
• Is it true that out of all bipartite graphs, crown graphs require longest word-representants?
• Is the line graph of a non-word-representable graph always non-word-representable?
• Which (hard) problems on graphs can be translated to words representing them and solved on words (efficiently)?

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