On the Existence of Word-representable Line Graphs of Non-word-representable Graphs
An open question in the theory of word-representable graphs for the past decade has been whether the line graph of a non-word-representable graph is always non-word-representable. By formulating an appropriate optimization problem for the decision problem of 3-semi-transitive graphs, we show that th...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
05.08.2021
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| Abstract | An open question in the theory of word-representable graphs for the past
decade has been whether the line graph of a non-word-representable graph is
always non-word-representable. By formulating an appropriate optimization
problem for the decision problem of 3-semi-transitive graphs, we show that the
line graph of a non-word-representable graph can be word-representable. Using
IBM's CPLEX solver, we demonstrate for several known word-representable and
non-word-representable graphs that the line graph of a graph is
3-semi-transitive when there is a solution to the optimization problem. This
results in an example where the line graph of a non-word-representable graph is
both 3-semi-transitive and semi-transitive and thus is word-representable. |
|---|---|
| AbstractList | An open question in the theory of word-representable graphs for the past
decade has been whether the line graph of a non-word-representable graph is
always non-word-representable. By formulating an appropriate optimization
problem for the decision problem of 3-semi-transitive graphs, we show that the
line graph of a non-word-representable graph can be word-representable. Using
IBM's CPLEX solver, we demonstrate for several known word-representable and
non-word-representable graphs that the line graph of a graph is
3-semi-transitive when there is a solution to the optimization problem. This
results in an example where the line graph of a non-word-representable graph is
both 3-semi-transitive and semi-transitive and thus is word-representable. |
| Author | Akrobotu, P D Akbar, M M Brewer, C P |
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| BackLink | https://doi.org/10.48550/arXiv.2108.02363$$DView paper in arXiv |
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| Snippet | An open question in the theory of word-representable graphs for the past
decade has been whether the line graph of a non-word-representable graph is
always... |
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| SubjectTerms | Mathematics - Combinatorics |
| Title | On the Existence of Word-representable Line Graphs of Non-word-representable Graphs |
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