Parameterized Algorithms for Book Embedding Problems
A $k$-page book embedding of a graph $G$ draws the vertices of $G$ on a line and the edges on $k$ half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether $G$ admits a $k$-page book embedding both when the linear orde...
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| Published in: | Journal of graph algorithms and applications Vol. 24; no. 4; pp. 603 - 620 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.12.2020
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| ISSN: | 1526-1719, 1526-1719 |
| Online Access: | Get full text |
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| Summary: | A $k$-page book embedding of a graph $G$ draws the vertices of $G$ on a line and the edges on $k$ half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether $G$ admits a $k$-page book embedding both when the linear order of the vertices is fixed, called ${\rm F{\small IXED}-O{\small RDER}~B{\small OOK}~T{\small HICKNESS}}$, or not fixed, called ${\rm B{\small OOK}~T{\small HICKNESS}}$. Both problems are known to be ${\sf NP}$-complete in general. We show that ${\rm F{\small IXED}-O{\small RDER}~B{\small OOK}~T{\small HICKNESS}}$ and ${\rm B{\small OOK}~T{\small HICKNESS}}$ are fixed-parameter tractable parameterized by the vertex cover number of the graph and that ${\rm F{\small IXED}-O{\small RDER}~B{\small OOK}~T{\small HICKNESS}}$ is fixed-parameter tractable parameterized by the pathwidth of the vertex order. |
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| ISSN: | 1526-1719 1526-1719 |
| DOI: | 10.7155/jgaa.00526 |