Matches in SemOpenAlex for { <https://semopenalex.org/work/W2997483836> ?p ?o ?g. }
Showing items 1 to 93 of
93
with 100 items per page.
- W2997483836 abstract "For two graphs $G$ and $H$, write $G stackrel{mathrm{rbw}}{longrightarrow} H$ if $G$ has the property that every {sl proper} colouring of its edges admits a {sl rainbow} copy of $H$. We study the thresholds for such so called {sl anti-Ramsey} properties in randomly perturbed dense graphs, by which we mean unions of the form $G cup mathbb{G}(n,p)$, where $G$ is an $n$-vertex graph with edge-density $d$, the latter being independent of $n$. For complete graphs, we determine the threshold for the property $G cup mathbb{G}(n,p) stackrel{mathrm{rbw}}{longrightarrow} K_{2r-1}$ for all $rgeq 2$. In particular, if $r geq 5$, then this threshold is $n^{-1/m_2(K_r)}$. For complete graphs of even order, we prove that the property $G cup mathbb{G}(n,p) stackrel{mathrm{rbw}}{longrightarrow} K_{2r}$ holds a.a.s. whenever $r geq 4$ and $p := p(n) = omega left(n^{-(r-2)/binom{r}{2}} right)$. We conjecture, that for every $r geq 5$, the threshold for the property $G cup mathbb{G}(n,p) stackrel{mathrm{rbw}}{longrightarrow} K_{2r}$ is $n^{-1/m_2(K_r)}$ (the latter is easily seen to be a lower bound for this threshold). We believe that $n^{-1/m_2(K_r)}$ is not the threshold for the property $G cup mathbb{G}(n,p) stackrel{mathrm{rbw}}{longrightarrow} K_{2r}$ whenever $r leq 4$. Clearly, no random edges are needed for $r=1$. For $r=2$, we prove that the threshold is $n^{-5/4}$. Lastly, we prove that for every $ell geq 1$, the threshold of the property $G cup mathbb{G}(n,p) stackrel{mathrm{rbw}}{longrightarrow} C_{2ell+1}$ is $n^{-2}$; in particular, it does not depend on the length of the cycle (clearly, for even cycles, no random perturbation is needed)." @default.
- W2997483836 created "2020-01-10" @default.
- W2997483836 creator A5001435782 @default.
- W2997483836 creator A5029280195 @default.
- W2997483836 creator A5072848658 @default.
- W2997483836 date "2019-12-31" @default.
- W2997483836 modified "2023-09-27" @default.
- W2997483836 title "Anti-Ramsey properties of randomly perturbed dense graphs" @default.
- W2997483836 cites W1518503060 @default.
- W2997483836 cites W2015373594 @default.
- W2997483836 cites W2033599053 @default.
- W2997483836 cites W2034838716 @default.
- W2997483836 cites W2058619174 @default.
- W2997483836 cites W2064298921 @default.
- W2997483836 cites W2067023564 @default.
- W2997483836 cites W2097225291 @default.
- W2997483836 cites W2123293563 @default.
- W2997483836 cites W2171469198 @default.
- W2997483836 cites W2615363413 @default.
- W2997483836 cites W2907936830 @default.
- W2997483836 cites W2911850936 @default.
- W2997483836 cites W2912404715 @default.
- W2997483836 cites W2962757025 @default.
- W2997483836 cites W2962779128 @default.
- W2997483836 cites W2963959484 @default.
- W2997483836 cites W2964241396 @default.
- W2997483836 cites W2964263579 @default.
- W2997483836 cites W2977660455 @default.
- W2997483836 cites W2978236022 @default.
- W2997483836 cites W2987824872 @default.
- W2997483836 cites W3015052924 @default.
- W2997483836 cites W3018741894 @default.
- W2997483836 cites W3144881883 @default.
- W2997483836 cites W2787372031 @default.
- W2997483836 hasPublicationYear "2019" @default.
- W2997483836 type Work @default.
- W2997483836 sameAs 2997483836 @default.
- W2997483836 citedByCount "0" @default.
- W2997483836 crossrefType "posted-content" @default.
- W2997483836 hasAuthorship W2997483836A5001435782 @default.
- W2997483836 hasAuthorship W2997483836A5029280195 @default.
- W2997483836 hasAuthorship W2997483836A5072848658 @default.
- W2997483836 hasConcept C10138342 @default.
- W2997483836 hasConcept C114614502 @default.
- W2997483836 hasConcept C118615104 @default.
- W2997483836 hasConcept C121332964 @default.
- W2997483836 hasConcept C132525143 @default.
- W2997483836 hasConcept C162324750 @default.
- W2997483836 hasConcept C182306322 @default.
- W2997483836 hasConcept C2779557605 @default.
- W2997483836 hasConcept C2780990831 @default.
- W2997483836 hasConcept C33923547 @default.
- W2997483836 hasConcept C62520636 @default.
- W2997483836 hasConcept C80899671 @default.
- W2997483836 hasConceptScore W2997483836C10138342 @default.
- W2997483836 hasConceptScore W2997483836C114614502 @default.
- W2997483836 hasConceptScore W2997483836C118615104 @default.
- W2997483836 hasConceptScore W2997483836C121332964 @default.
- W2997483836 hasConceptScore W2997483836C132525143 @default.
- W2997483836 hasConceptScore W2997483836C162324750 @default.
- W2997483836 hasConceptScore W2997483836C182306322 @default.
- W2997483836 hasConceptScore W2997483836C2779557605 @default.
- W2997483836 hasConceptScore W2997483836C2780990831 @default.
- W2997483836 hasConceptScore W2997483836C33923547 @default.
- W2997483836 hasConceptScore W2997483836C62520636 @default.
- W2997483836 hasConceptScore W2997483836C80899671 @default.
- W2997483836 hasLocation W29974838361 @default.
- W2997483836 hasOpenAccess W2997483836 @default.
- W2997483836 hasPrimaryLocation W29974838361 @default.
- W2997483836 hasRelatedWork W1542986919 @default.
- W2997483836 hasRelatedWork W2018169836 @default.
- W2997483836 hasRelatedWork W2026063626 @default.
- W2997483836 hasRelatedWork W2029077819 @default.
- W2997483836 hasRelatedWork W2259590107 @default.
- W2997483836 hasRelatedWork W2279361354 @default.
- W2997483836 hasRelatedWork W269900985 @default.
- W2997483836 hasRelatedWork W2735940686 @default.
- W2997483836 hasRelatedWork W2794641614 @default.
- W2997483836 hasRelatedWork W2896199580 @default.
- W2997483836 hasRelatedWork W2900330833 @default.
- W2997483836 hasRelatedWork W2912404715 @default.
- W2997483836 hasRelatedWork W2949091650 @default.
- W2997483836 hasRelatedWork W2949154825 @default.
- W2997483836 hasRelatedWork W2952110075 @default.
- W2997483836 hasRelatedWork W2962811018 @default.
- W2997483836 hasRelatedWork W2963958519 @default.
- W2997483836 hasRelatedWork W2982382916 @default.
- W2997483836 hasRelatedWork W3200271267 @default.
- W2997483836 hasRelatedWork W3201982285 @default.
- W2997483836 isParatext "false" @default.
- W2997483836 isRetracted "false" @default.
- W2997483836 magId "2997483836" @default.
- W2997483836 workType "article" @default.