10 research outputs found
Tight lower bounds on the number of bicliques in false-twin-free graphs
A \emph{biclique} is a maximal bipartite complete induced subgraph of .
Bicliques have been studied in the last years motivated by the large number of
applications. In particular, enumeration of the maximal bicliques has been of
interest in data analysis. Associated with this issue, bounds on the maximum
number of bicliques were given. In this paper we study bounds on the minimun
number of bicliques of a graph. Since adding false-twin vertices to does
not change the number of bicliques, we restrict to false-twin-free graphs. We
give a tight lower bound on the minimum number bicliques for a subclass of
,false-twin-free graphs and for the class of
,false-twin-free graphs. Finally we discuss the problem for general
graphs.Comment: 16 pages, 4 figue
Twin-width VIII: delineation and win-wins
We introduce the notion of delineation. A graph class is said
delineated if for every hereditary closure of a subclass of
, it holds that has bounded twin-width if and only if
is monadically dependent. An effective strengthening of
delineation for a class implies that tractable FO model checking
on is perfectly understood: On hereditary closures of
subclasses of , FO model checking is fixed-parameter tractable
(FPT) exactly when has bounded twin-width. Ordered graphs
[BGOdMSTT, STOC '22] and permutation graphs [BKTW, JACM '22] are effectively
delineated, while subcubic graphs are not. On the one hand, we prove that
interval graphs, and even, rooted directed path graphs are delineated. On the
other hand, we show that segment graphs, directed path graphs, and visibility
graphs of simple polygons are not delineated. In an effort to draw the
delineation frontier between interval graphs (that are delineated) and
axis-parallel two-lengthed segment graphs (that are not), we investigate the
twin-width of restricted segment intersection classes. It was known that
(triangle-free) pure axis-parallel unit segment graphs have unbounded
twin-width [BGKTW, SODA '21]. We show that -free segment graphs, and
axis-parallel -free unit segment graphs have bounded twin-width, where
is the half-graph or ladder of height . In contrast, axis-parallel
-free two-lengthed segment graphs have unbounded twin-width. Our new
results, combined with the known FPT algorithm for FO model checking on graphs
given with -sequences, lead to win-win arguments. For instance, we derive
FPT algorithms for -Ladder on visibility graphs of 1.5D terrains, and
-Independent Set on visibility graphs of simple polygons.Comment: 51 pages, 19 figure
Efficient discovery of binding motif pairs from protein-protein interactions
Ph.DDOCTOR OF PHILOSOPH
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Enumerating maximal bicliques in bipartite graphs with favorable degree sequences
We propose an output-sensitive algorithm for the enumeration of all maximal bicliques in a bipartite graph, tailored to the case when the degree distribution in one partite set is very skewed. We accomplish a worst-case bound better than previously known general bounds if, e.g., the degree sequence
follows a power law
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum