Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Czabarka, Eva"'
Autor:
Cabello, Sergio, Czabarka, Éva, Fabila-Monroy, Ruy, Higashikawa, Yuya, Seidel, Raimund, Székely, László, Tkadlec, Josef, Wesolek, Alexandra
Let $S$ be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of $S$ with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probabilit
Externí odkaz:
http://arxiv.org/abs/2312.01935
Autor:
Clifton, Ann, Czabarka, Eva, Dossou-Olory, Audace, Liu, Kevin, Loeb, Sarah, Okur, Utku, Szekely, Laszlo, Wicke, Kristina
We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees of $T$. O
Externí odkaz:
http://arxiv.org/abs/2311.02255
Autor:
Clifton, Ann, Czabarka, Eva, Liu, Kevin, Loeb, Sarah, Okur, Utku, Szekely, Laszlo, Wicke, Kristina
We provide an $\Omega(n\log n) $ lower bound and an $O(n^2)$ upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted binary trees with $n$ leaves, i.e., contain all of them as induced
Externí odkaz:
http://arxiv.org/abs/2308.06580
A tanglegram $\cal T$ consists of two rooted binary trees with the same number of leaves, and a perfect matching between the two leaf sets. In a layout, the tanglegrams is drawn with the leaves on two parallel lines, the trees on either side of the s
Externí odkaz:
http://arxiv.org/abs/2307.04309
P. Erd\H{o}s, J. Pach, R. Pollack, and Z. Tuza [J. Combin. Theory, B 47 (1989), 279--285] made conjectures for the maximum diameter of connected graphs without a complete subgraph $K_{k+1}$, which have order $n$ and minimum degree $\delta$. Settling
Externí odkaz:
http://arxiv.org/abs/2109.13887
Erd\H{o}s, Pach, Pollack and Tuza [J. Combin. Theory, B 47, (1989), 279-285] conjectured that the diameter of a $K_{2r}$-free connected graph of order $n$ and minimum degree $\delta\geq 2$ is at most $\frac{2(r-1)(3r+2)}{(2r^2-1)}\cdot \frac{n}{\delt
Externí odkaz:
http://arxiv.org/abs/2009.02611
Contrary to the expectation arising from the tanglegram Kuratowski theorem of \'E. Czabarka, L.A. Sz\'ekely and S. Wagner [SIAM J. Discrete Math. 31(3): 1732--1750, (2017)], we construct an infinite antichain of planar tanglegrams with respect to the
Externí odkaz:
http://arxiv.org/abs/2007.06091
The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide formulae for the minimum Wiener index of simple triangulations and quadrangulations with connectivity at least $c$, and provide the
Externí odkaz:
http://arxiv.org/abs/2003.03873
Let $ G $ be a connected graph. If $\bar{\sigma}(v)$ denotes the arithmetic mean of the distances from $v$ to all other vertices of $G$, then the proximity, $\pi(G)$, of $G$ is defined as the smallest value of $\bar{\sigma}(v)$ over all vertices $v$
Externí odkaz:
http://arxiv.org/abs/2001.09012
We find the asymptotic behavior of the Steiner k-diameter of the $n$-cube if $k$ is large. Our main contribution is the lower bound, which utilizes the probabilistic method.
Externí odkaz:
http://arxiv.org/abs/1907.07546