Results 61 to 70 of about 1,906 (145)

Long induced paths in graphs

, 2016
We prove that every 3-connected planar graph on $n$ vertices contains an induced path on $\Omega(\log n)$ vertices, which is best possible and improves the best known lower bound by a multiplicative factor of $\log \log n$.
Esperet, Louis, Lemoine, Laetitia, Maffray, Frédéric   +2 more
core   +3 more sources

The product structure of squaregraphs

Journal of Graph Theory, Volume 105, Issue 2, Page 179-191, February 2024.
Abstract A squaregraph is a plane graph in which each internal face is a 4‐cycle and each internal vertex has degree at least 4. This paper proves that every squaregraph is isomorphic to a subgraph of the semistrong product of an outerplanar graph and a path.
Robert Hickingbotham, Paul Jungeblut, Laura Merker, David R. Wood   +3 more
wiley   +1 more source

Equal Entries in Totally Positive Matrices [PDF]

, 2013
We show that the maximal number of equal entries in a totally positive (resp. totally nonsingular) $n\textrm{-by-}n$ matrix is $\Theta(n^{4/3})$ (resp. $\Theta(n^{3/2}$)).
Farber, Miriam, Faulk, Mitchell, Johnson, Charles R., Marzion, Evan   +3 more
core  

Clusters of Cycles

, 2001
A {\it cluster of cycles} (or {\it $(r,q)$-polycycle}) is a simple planar 2--co nnected finite or countable graph $G$ of girth $r$ and maximal vertex-degree $q$, which admits {\it $(r,q)$-polycyclic realization} on the plane, denote it by $P(G)$, i.e ...
Archdeacon, Balaban, Bousquet-Mélou, Chepoi, Conway, Cyvin, Deza, Deza, Deza, Deza, Harary, Harborth, Michel Deza, Mikhail Shtogrin, Shtogrin, Shtogrin   +15 more
core   +2 more sources

Bipartite Minors [PDF]

, 2013
We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain $K_{3,3}$ as a bipartite minor.
Chudnovsky, Maria, Kalai, Gil, Nevo, Eran, Novik, Isabella, Seymour, Paul   +4 more
core   +1 more source

The role of twins in computing planar supports of hypergraphs

, 2020
A support or realization of a hypergraph $H$ is a graph $G$ on the same vertex as $H$ such that for each hyperedge of $H$ it holds that its vertices induce a connected subgraph of $G$.
Kanj, Iyad A., Komusiewicz, Christian, Niedermeier, Rolf, Sorge, Manuel, van Bevern, René   +4 more
core  

Maximal outerplanar graphs as chordal graphs, path-neighborhood graphs, and triangle graphs [PDF]

Maximal outerplanar graphs are characterized using three different classes of graphs. A path-neighborhood graph is a connected graph in which every neighborhood induces a path. The triangle graph $T(G)$ has the triangles of the graph $G$ as its vertices,
Laskar, R.C., Mulder, H.M., Novick, B.
core   +1 more source

Storage Capacity as an Information-Theoretic Vertex Cover and the Index Coding Rate

, 2017
Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from
Mazumdar, Arya, McGregor, Andrew, Vorotnikova, Sofya   +2 more
core   +1 more source

Graphs with Plane Outside-Obstacle Representations [PDF]

, 2013
An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent.
Koch, Alexander, Krug, Marcus, Rutter, Ignaz   +2 more
core  

k-TRIANGULAR PRIME CORDIAL LABELING OF MAXIMAL OUTERPLANAR GRAPHS [PDF]

, 2022
G. Megala, K. Annadurai
openalex   +1 more source