Results 11 to 20 of about 1,483,849 (194)
Anti-Ramsey threshold of cycles [PDF]
Discrete Applied Mathematics, 2022 For graphs $G$ and $H$, let $G \overset{\mathrm{rb}}{\longrightarrow} H$ denote the property that for every proper edge colouring of $G$ there is a rainbow copy of $H$ in $G$. Extending a result of Nenadov, Person, Škorić and Steger [J. Combin. Theory Ser. B 124 (2017),1-38], we determine the threshold for $G(n,p) \overset{\mathrm{rb}}{\longrightarrow}
Gabriel Ferreira Barros +3 more
openaire +3 more sources
Thresholds for constrained Ramsey and anti-Ramsey problems
European Journal of CombinatoricsLet $H_1$ and $H_2$ be graphs. A graph $G$ has the constrained Ramsey property for $(H_1,H_2)$ if every edge-colouring of $G$ contains either a monochromatic copy of $H_1$ or a rainbow copy of $H_2$.
Behague, Natalie +4 more
core +2 more sources
Anti-Ramsey Multiplicities [PDF]
Australas. J Comb., 2018 The Ramsey multiplicity constant of a graph $H$ is the minimum proportion of copies of $H$ in the complete graph which are monochromatic under an edge-coloring of $K_n$ as $n$ goes to infinity. Graphs for which this minimum is asymptotically achieved by taking a random coloring are called {\em common}, and common graphs have been studied extensively ...
Jessica De Silva +5 more
openaire +3 more sources
Size and Degree Anti-Ramsey Numbers [PDF]
Graphs and Combinatorics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gang Chen, Yongxin Lan, Zi-Xia Song
+10 more sources
Geophysical Monograph Series, Page 1-26., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Richard E. Ernst +8 more
wiley +1 more source
The anti-Ramsey problem for the Sidon equation [PDF]
Discrete Mathematics, 2019 For $n \geq k \geq 4$, let $AR_{X + Y = Z + T}^k (n)$ be the maximum number of rainbow solutions to the Sidon equation $X+Y = Z + T$ over all $k$-colorings $c:[n] \rightarrow [k]$. It can be shown that the total number of solutions in $[n]$ to the Sidon equation is $n^3/12 + O(n^2)$ and so, trivially, $AR_{X+Y = Z + T}^k (n) \leq n^3 /12 + O (n^2)$. We
Vladislav Taranchuk, Craig Timmons
openaire +2 more sources
On an anti‐Ramsey property of Ramanujan graphs [PDF]
Random Structures & Algorithms, 1995 AbstractIf G and H are graphs, we write G→ H (respectively, G→ TH) if for any proper edge‐coloring γ of G there is a subgraph H' ⊂ G of G isomorphic to H (respectively, isomorphic to a subdivision of H) such that γ is injective on E(H'). Let us write Cl for the cycle of length l. Spencer (cf.
Penny E. Haxell, Yoshiharu Kohayakawa
openaire +1 more source
Journal of Combinatorial Theory, Series B, 1995 It is shown that for every \(\ell \geq 3\) there exists a graph \(G\) of girth \(\ell\) such that in any proper edge-colouring of \(G\) one may find a cycle of length \(\ell\) all of whose edges are given different colours. This result settles a particular case of a conjecture of Rödl and Tuza [\textit{V. Rödl} and \textit{Zs.
Yoshiharu Kohayakawa, Tomasz Luczak 0001
openaire +1 more source
The anti-Ramsey threshold of complete graphs
Discrete Mathematics, 2023 For graphs $G$ and $H$, let $G {\displaystyle\smash{\begin{subarray}{c} \hbox{$\tiny\rm rb$} \\ \longrightarrow \\ \hbox{$\tiny\rm p$} \end{subarray}}}H$ denote the property that for every proper edge-colouring of $G$ there is a rainbow $H$ in $G$. It is known that, for every graph $H$, an asymptotic upper bound for the threshold function $p^{\rm rb}_H=
Yoshiharu Kohayakawa +3 more
openaire +2 more sources
An Anti-Ramsey Condition on Trees [PDF]
The Electronic Journal of Combinatorics, 2008 Let $H$ be a finite tree. We consider trees $T$ such that if the edges of $T$ are colored so that no color occurs more than $b$ times, then $T$ has a subgraph isomorphic to $H$ in which no color is repeated. We will show that if $H$ falls into a few classes of trees, including those of diameter at most $4$, then the minimum value of $e(T)$ is provided
openaire +3 more sources