On the General Position Number of Mycielskian Graphs
The general position problem for graphs was inspired by the no-three-in-line problem from discrete geometry. A set $S$ of vertices of a graph $G$ is a \emph{general position set} if no shortest path in $G$ contains three or more vertices of $S$. The \emph{general position number} of $G$ is the numbe...
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| creator | Thomas, Elias John Chandran, Ullas Tuite, James Di Stefano, Gabriele |
| description | The general position problem for graphs was inspired by the no-three-in-line
problem from discrete geometry. A set $S$ of vertices of a graph $G$ is a
\emph{general position set} if no shortest path in $G$ contains three or more
vertices of $S$. The \emph{general position number} of $G$ is the number of
vertices in a largest general position set. In this paper we investigate the
general position numbers of the Mycielskian of graphs. We give tight upper and
lower bounds on the general position number of the Mycielskian of a graph $G$
and investigate the structure of the graphs meeting these bounds. We determine
this number exactly for common classes of graphs, including cubic graphs and a
wide range of trees. |
| doi_str_mv | 10.48550/arxiv.2203.08170 |
| format | Article |
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problem from discrete geometry. A set $S$ of vertices of a graph $G$ is a
\emph{general position set} if no shortest path in $G$ contains three or more
vertices of $S$. The \emph{general position number} of $G$ is the number of
vertices in a largest general position set. In this paper we investigate the
general position numbers of the Mycielskian of graphs. We give tight upper and
lower bounds on the general position number of the Mycielskian of a graph $G$
and investigate the structure of the graphs meeting these bounds. We determine
this number exactly for common classes of graphs, including cubic graphs and a
wide range of trees.</description><identifier>DOI: 10.48550/arxiv.2203.08170</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2022-03</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2203.08170$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2203.08170$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Thomas, Elias John</creatorcontrib><creatorcontrib>Chandran, Ullas</creatorcontrib><creatorcontrib>Tuite, James</creatorcontrib><creatorcontrib>Di Stefano, Gabriele</creatorcontrib><title>On the General Position Number of Mycielskian Graphs</title><description>The general position problem for graphs was inspired by the no-three-in-line
problem from discrete geometry. A set $S$ of vertices of a graph $G$ is a
\emph{general position set} if no shortest path in $G$ contains three or more
vertices of $S$. The \emph{general position number} of $G$ is the number of
vertices in a largest general position set. In this paper we investigate the
general position numbers of the Mycielskian of graphs. We give tight upper and
lower bounds on the general position number of the Mycielskian of a graph $G$
and investigate the structure of the graphs meeting these bounds. We determine
this number exactly for common classes of graphs, including cubic graphs and a
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problem from discrete geometry. A set $S$ of vertices of a graph $G$ is a
\emph{general position set} if no shortest path in $G$ contains three or more
vertices of $S$. The \emph{general position number} of $G$ is the number of
vertices in a largest general position set. In this paper we investigate the
general position numbers of the Mycielskian of graphs. We give tight upper and
lower bounds on the general position number of the Mycielskian of a graph $G$
and investigate the structure of the graphs meeting these bounds. We determine
this number exactly for common classes of graphs, including cubic graphs and a
wide range of trees.</abstract><doi>10.48550/arxiv.2203.08170</doi><oa>free_for_read</oa></addata></record> |
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| title | On the General Position Number of Mycielskian Graphs |
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