Colorful Hamilton cycles in random graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929234512969728 |
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| author | Chakraborti, Debsoumya Frieze, Alan Hasabnis, Mihir |
| author_facet | Chakraborti, Debsoumya Frieze, Alan Hasabnis, Mihir |
| contents | Given an $n$ vertex graph whose edges have colored from one of $r$ colors $C=\{c_1,c_2,\ldots,c_r\}$, we define the Hamilton cycle color profile $hcp(G)$ to be the set of vectors $(m_1,m_2,\ldots,m_r)\in [0,n]^r$ such that there exists a Hamilton cycle that is the concatenation of $r$ paths $P_1,P_2,\ldots,P_r$, where $P_i$ contains $m_i$ edges of color $c_i$. We study $hcp(G_{n,p})$ when the edges are randomly colored. We discuss the profile close to the threshold for the existence of a Hamilton cycle and the threshold for when $hcp(G_{n,p})=\{(m_1,m_2,\ldots,m_r)\in [0,n]^r: m_1+m_2+\cdots+m_r=n\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_03916 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Colorful Hamilton cycles in random graphs Chakraborti, Debsoumya Frieze, Alan Hasabnis, Mihir Combinatorics Given an $n$ vertex graph whose edges have colored from one of $r$ colors $C=\{c_1,c_2,\ldots,c_r\}$, we define the Hamilton cycle color profile $hcp(G)$ to be the set of vectors $(m_1,m_2,\ldots,m_r)\in [0,n]^r$ such that there exists a Hamilton cycle that is the concatenation of $r$ paths $P_1,P_2,\ldots,P_r$, where $P_i$ contains $m_i$ edges of color $c_i$. We study $hcp(G_{n,p})$ when the edges are randomly colored. We discuss the profile close to the threshold for the existence of a Hamilton cycle and the threshold for when $hcp(G_{n,p})=\{(m_1,m_2,\ldots,m_r)\in [0,n]^r: m_1+m_2+\cdots+m_r=n\}$. |
| title | Colorful Hamilton cycles in random graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2103.03916 |