2 research outputs found
The Complexity of Helly- EPG Graph Recognition
Golumbic, Lipshteyn, and Stern defined in 2009 the class of EPG graphs, the
intersection graph class of edge paths on a grid. An EPG graph is a graph
that admits a representation where its vertices correspond to paths in a grid
, such that two vertices of are adjacent if and only if their
corresponding paths in have a common edge. If the paths in the
representation have at most bends, we say that it is a -EPG
representation. A collection of sets satisfies the Helly property when
every sub-collection of that is pairwise intersecting has at least one
common element. In this paper, we show that given a graph and an integer
, the problem of determining whether admits a -EPG representation
whose edge-intersections of paths satisfy the Helly property, so-called
Helly--EPG representation, is in NP, for every bounded by a polynomial
function of . Moreover, we show that the problem of recognizing
Helly--EPG graphs is NP-complete, and it remains NP-complete even when
restricted to 2-apex and 3-degenerate graphs
The Complexity of Helly- EPG Graph Recognition
Golumbic, Lipshteyn, and Stern defined in 2009 the class of EPG graphs, the
intersection graph class of edge paths on a grid. An EPG graph is a graph
that admits a representation where its vertices correspond to paths in a grid
, such that two vertices of are adjacent if and only if their
corresponding paths in have a common edge. If the paths in the
representation have at most bends, we say that it is a -EPG
representation. A collection of sets satisfies the Helly property when
every sub-collection of that is pairwise intersecting has at least one
common element. In this paper, we show that given a graph and an integer
, the problem of determining whether admits a -EPG representation
whose edge-intersections of paths satisfy the Helly property, so-called
Helly--EPG representation, is in NP, for every bounded by a polynomial
function of . Moreover, we show that the problem of recognizing
Helly--EPG graphs is NP-complete, and it remains NP-complete even when
restricted to 2-apex and 3-degenerate graphs