Geodesic
The Unit Bar Visibility Number of a Graph
Journal of Graph Algorithms and Applications, Tome 20 (2016) no. 2, pp. 269-297.

Voir la notice de l'article provenant de la source Journal of Graph Algorythms and Applications website

A $t$-unit-bar representation of a graph $G$ is an assignment of sets of at most $t$ horizontal unit-length segments in the plane to the vertices of $G$ so that (1) all of the segments are pairwise nonintersecting, and (2) two vertices $x$ and $y$ are adjacent if and only if there is a vertical channel of positive width connecting a segment assigned to $x$ and a segment assigned to $y$ that intersects no other segment. The unit bar visibility number of a graph $G$, denoted $ub(G)$, is the minimum $t$ such that $G$ has a $t$-unit-bar visibility representation. Our results include a linear time algorithm that determines $ub(T)$ when $T$ is a tree, bounds on $ub(K_{m,n})$ that determine $ub(K_{m,n})$ asymptotically when $n$ and $m$ are asymptotically equal, and bounds on $ub(K_n)$ that determine $ub(K_n)$ exactly when $n\equiv 1,2\pmod 6$
DOI : 10.7155/jgaa.00393
Keywords: visibility, visibility number, unit bar visibilty, 05C62 
@article{JGAA_2016_20_2_a4,
     author = {Emily Gaub and Michelle Rose and Paul Wenger},
     title = {The {Unit} {Bar} {Visibility} {Number} of a {Graph}},
     journal = {Journal of Graph Algorithms and Applications},
     pages = {269--297},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2016},
     doi = {10.7155/jgaa.00393},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00393/}
}
TY  - JOUR
AU  - Emily Gaub
AU  - Michelle Rose
AU  - Paul Wenger
TI  - The Unit Bar Visibility Number of a Graph
JO  - Journal of Graph Algorithms and Applications
PY  - 2016
SP  - 269
EP  - 297
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00393/
DO  - 10.7155/jgaa.00393
LA  - en
ID  - JGAA_2016_20_2_a4
ER  - 
%0 Journal Article
%A Emily Gaub
%A Michelle Rose
%A Paul Wenger
%T The Unit Bar Visibility Number of a Graph
%J Journal of Graph Algorithms and Applications
%D 2016
%P 269-297
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00393/
%R 10.7155/jgaa.00393
%G en
%F JGAA_2016_20_2_a4
Emily Gaub; Michelle Rose; Paul Wenger. The Unit Bar Visibility Number of a Graph. Journal of Graph Algorithms and Applications, Tome 20 (2016) no. 2, pp. 269-297. doi : 10.7155/jgaa.00393. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00393/

Cité par Sources :