Results 31 to 40 of about 274 (48)
Improved bounds for the crossing numbers of K_m,n and K_n
, 2004 It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing
de Klerk, E. +4 more
core +2 more sources
Archimedean tiling graphs with Gallai’s property
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 Gallai in 1966 raised the question about the existence of graphs with the property that every vertex is missed by some longest path. This property will be called Gallai’s property.
Chang Zhikui, Yuan Liping
doaj +1 more source
Graph connectivity and universal rigidity of bar frameworks [PDF]
, 2014 Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \leq r \leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally rigid.
Alfakih, A. Y.
core
Clique trees of infinite locally finite chordal graphs [PDF]
, 2018 We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees.
Hofer-Temmel, Christoph, Lehner, Florian
core +1 more source
No finite $5$-regular matchstick graph exists [PDF]
, 2014 A graph $G=(V,E)$ is called a unit-distance graph in the plane if there is an injective embedding of $V$ in the plane such that every pair of adjacent vertices are at unit distance apart.
Kurz, Sascha
core
A Consistent Histogram Estimator for Exchangeable Graph Models [PDF]
, 2014 Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue.
Airoldi, Edoardo M., Chan, Stanley H.
core
Fullerenes with the maximum Clar number [PDF]
, 2014 The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2.
Gao, Yang, Li, Qiuli, Zhang, Heping
core
The rectilinear local crossing number of $K_n$
, 2017 We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \}, $ \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3}{3}
Fernández-Merchant, Silvia +1 more
core
Combinatorial Properties and Recognition of Unit Square Visibility Graphs. [PDF]
Discrete Comput Geom, 2023 Casel K +4 more
europepmc +1 more source
Best match graphs and reconciliation of gene trees with species trees. [PDF]
J Math Biol, 2020 Geiß M +6 more
europepmc +1 more source