Zobrazeno 1 - 10
of 190
pro vyhledávání: '"Martin, Ryan R"'
Autor:
Gomez-Leos, Enrique, Martin, Ryan R.
A perfect $H$-tiling in a graph $G$ is a collection of vertex-disjoint copies of a graph $H$ in $G$ that covers all vertices of $G$. Motivated by papers of Bush and Zhao and of Balogh, Treglown, and Wagner, we determine the threshold for the existenc
Externí odkaz:
http://arxiv.org/abs/2411.12738
Autor:
Baker, Dustin, Gomez-Leos, Enrique, Halfpap, Anastasia, Heath, Emily, Martin, Ryan R., Miller, Joe, Parker, Alex, Pungello, Hope, Schwieder, Coy, Veldt, Nick
Given a graph $H$, we say a graph $G$ is properly rainbow $H$-saturated if there is a proper edge-coloring of $G$ which contains no rainbow copy of $H$, but adding any edge to $G$ makes such an edge-coloring impossible. The proper rainbow saturation
Externí odkaz:
http://arxiv.org/abs/2409.15258
Autor:
Martin, Ryan R., Patkós, Balázs
A classical result of Kleitman determines the maximum number $f(n,s)$ of subsets in a family $\mathcal{F}\subseteq 2^{[n]}$ of sets that do not contain distinct sets $F_1,F_2,\dots,F_s$ that are pairwise disjoint in the case $n\equiv 0,-1$ (mod $s$).
Externí odkaz:
http://arxiv.org/abs/2409.08694
Autor:
Martin, Ryan R, Veldt, Nick
Given a set $X$, the power set $\mathbb{P}(X)$, and a finite poset $P$, a family $F\subset \mathbb{P}(X)$ is said to be induced-$P$-free if there is no injection $\phi: P\rightarrow \mathbb{P}(X)$ such that $\phi(p)\subseteq\phi(q)$ if and only if $p
Externí odkaz:
http://arxiv.org/abs/2408.14648
A coloring of the edges of a graph $G$ in which every $K_{1,2}$ is totally multicolored is known as a proper coloring and a coloring of the edges of $G$ in which every $K_{1,2}$ and every $K_{2,2}$ is totally multicolored is called a B-coloring. In t
Externí odkaz:
http://arxiv.org/abs/2408.09081
We call a proper edge coloring of a graph $G$ a B-coloring if every 4-cycle of $G$ is colored with four different colors. Let $q_B(G)$ denote the smallest number of colors needed for a B-coloring of $G$. Motivated by earlier papers on B-colorings, he
Externí odkaz:
http://arxiv.org/abs/2408.09059
Autor:
Martin, Ryan R., Patkós, Balázs
The Erd\H os Matching Conjecture states that the maximum size $f(n,k,s)$ of a family $\mathcal{F}\subseteq \binom{[n]}{k}$ that does not contain $s$ pairwise disjoint sets is $\max\{|\mathcal{A}_{k,s}|,|\mathcal{B}_{n,k,s}|\}$, where $\mathcal{A}_{k,
Externí odkaz:
http://arxiv.org/abs/2404.12971
Autor:
Martin, Ryan R., Veldt, Nick
Given a set $X$, a collection $\mathcal{F} \subset \mathcal{P}(X)$ is said to be $k$-Sperner if it does not contain a chain of length $k+1$ under set inclusion and it is saturated if it is maximal with respect to this probability. Gerbner et al. prov
Externí odkaz:
http://arxiv.org/abs/2402.14113
How many copies of a fixed odd cycle, $C_{2m+1}$, can a planar graph contain? We answer this question asymptotically for $m\in\{2,3,4\}$ and prove a bound which is tight up to a factor of $3/2$ for all other values of $m$. This extends the prior resu
Externí odkaz:
http://arxiv.org/abs/2307.00116
A graph is cubical if it is a subgraph of a hypercube. For a cubical graph $H$ and a hypercube $Q_n$, $ex(Q_n, H)$ is the largest number of edges in an $H$-free subgraph of $Q_n$. If $ex(Q_n, H)$ is equal to a positive proportion of the number of edg
Externí odkaz:
http://arxiv.org/abs/2303.15529