Carath$é$odory Number and Exchange Number in $Δ$-convexity
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913782561767424 |
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| author | Anand, Bijo S. Anil, Arun Changat, Manoj Narasimha-Shenoi, Prasanth G. Ramla, Sabeer S. |
| author_facet | Anand, Bijo S. Anil, Arun Changat, Manoj Narasimha-Shenoi, Prasanth G. Ramla, Sabeer S. |
| contents | Given a graph $G$, a set is $Δ$-convex if there is no vertex $u\in V(G)\setminus S$ forming a triangle with two vertices of $S$. The $Δ$-convex hull of $S$ is the minimum $Δ$-convex set containing $S$. This article is an attempt to discuss the Carathéodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and, lexicographic products of graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_15025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Carath$é$odory Number and Exchange Number in $Δ$-convexity Anand, Bijo S. Anil, Arun Changat, Manoj Narasimha-Shenoi, Prasanth G. Ramla, Sabeer S. Combinatorics 05C38, 05C76, 05C99, 52A01 Given a graph $G$, a set is $Δ$-convex if there is no vertex $u\in V(G)\setminus S$ forming a triangle with two vertices of $S$. The $Δ$-convex hull of $S$ is the minimum $Δ$-convex set containing $S$. This article is an attempt to discuss the Carathéodory number and exchange number on various graph families and standard graph products namely Cartesian, strong and, lexicographic products of graphs. |
| title | Carath$é$odory Number and Exchange Number in $Δ$-convexity |
| topic | Combinatorics 05C38, 05C76, 05C99, 52A01 |
| url | https://arxiv.org/abs/2501.15025 |