A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Recognizing Helly Edge-Path-Tree graphs and their clique graphs

2011
*
Discrete Applied Mathematics
*

We present a unifying procedure for

doi:10.1016/j.dam.2011.02.008
fatcat:crnsduwvq5fvnf3xqns3un4s3a
*recognizing*intersection*graphs*of*Helly*families of paths in a tree and their*clique**graphs*. ... The*Helly*property makes it possible to look at these recognition problems as variants of the*Graph*Realization Problem, namely, the problem of*recognizing*Edge-Path-Tree matrices. ... the class of*clique*-*graphs*of class G. A*graph*is*clique*-*Helly*if K(G) is*Helly*. It is hereditary*clique*-*Helly*if each induced subgraph of G is*clique*-*Helly*. ...##
###
Faster recognition of clique-Helly and hereditary clique-Helly graphs

2007
*
Information Processing Letters
*

The best algorithms currently known to

doi:10.1016/j.ipl.2007.02.017
fatcat:437fimvx4rctljtdeh6mtxgbie
*recognize**clique*-*Helly*and hereditary*clique*-*Helly**graphs*have complexities O(nm 2 ) and O(n 2 m), respectively for a*graph*with n vertices and m edges. ... A*graph*G is*clique*-*Helly*when the family of its (maximal)*cliques*is*Helly*, while G is hereditary*clique*-*Helly*when every induced subgraph of it is*clique*-*Helly*. ... Currently known algorithms*recognize**clique*-*Helly**graphs*in O(nm 2 ) time, and hereditary*clique*-*Helly*in O(n 2 m) time. ...##
###
Computational aspects of the Helly property: a survey

2006
*
Journal of the Brazilian Computer Society
*

In 1923, Eduard

doi:10.1590/s0104-65002006000200002
fatcat:xoccurn6tnctpdyxuphsvnhsgy
*Helly*published his celebrated theorem, which originated the well known*Helly*property. ... In this work, we survey computational aspects of the*Helly*property. The main focus is algorithmic. ... Theorem 3.5 [28]*CLIQUE*-*HELLY*SANDWICH*GRAPH*is NP-complete. Disk-*Helly**graphs*Disk-*Helly**graphs*can also be*recognized*in polynomial time. ...##
###
Computational aspects of the Helly property: a survey

2006
*
Journal of the Brazilian Computer Society
*

In 1923, Eduard

doi:10.1007/bf03192385
fatcat:g576bhjqfbbdhhbqxgaodx2aiy
*Helly*published his celebrated theorem, which originated the well known*Helly*property. ... In this work, we survey computational aspects of the*Helly*property. The main focus is algorithmic. ... Theorem 3.5 [28]*CLIQUE*-*HELLY*SANDWICH*GRAPH*is NP-complete. Disk-*Helly**graphs*Disk-*Helly**graphs*can also be*recognized*in polynomial time. ...##
###
Complexity Aspects of the Helly Property: Graphs and Hypergraphs

2009
*
Electronic Journal of Combinatorics
*

In this work, we survey complexity aspects of the

doi:10.37236/38
fatcat:kqezaclnwbddraypsil6n5ltry
*Helly*property. The main focus is on characterizations of several classes of*graphs*and hypergraphs related to the*Helly*property. ... In 1923, Eduard*Helly*published his celebrated theorem, which originated the well known*Helly*property. ... Hence, G is a (p, q)-*clique*-*Helly**graph*. From the above theorem one can*recognize*(p, q)-*clique*-*Helly**graphs*in polynomial time if p and q are fixed. ...##
###
On the strong p-Helly property

2008
*
Discrete Applied Mathematics
*

Further, we apply the concept of strong p-

doi:10.1016/j.dam.2007.05.047
fatcat:ly2qavmkpjclfhb6jki5hi3zda
*Helly*hypergraphs to the*cliques*of a*graph*, leading to the class of strong p-*clique*-*Helly**graphs*. ... For p = 2, this class is equivalent to that of hereditary*clique*-*Helly**graphs*[E. Prisner, Hereditary*clique*-*Helly**graphs*, J. Combin. Math. Combin. Comput. 14 (1993) 216-220]. ... Similarly, the algorithm for*recognizing*p-*clique*-*Helly**graphs*is not suitable for*recognizing*hereditary p-*clique*-*Helly**graphs*either, because the number of induced subgraphs may also be exponential in ...##
###
Characterization and recognition of Helly circular-arc clique-perfect graphs

2005
*
Electronic Notes in Discrete Mathematics
*

In this work we characterize

doi:10.1016/j.endm.2005.06.026
fatcat:2wkk25kfp5a6zlmf7pgqkw5ddi
*clique*-perfect*graphs*by a restricted list of minimal forbidden induced subgraphs when the*graph*is a*Helly*circular-arc*graph*. ... A*clique*-transversal of a*graph*G is a subset of vertices that meets all the*cliques*of G. A*clique*-independent set is a collection of pairwise vertex-disjoint*cliques*. ... A*graph*is*clique*-*Helly*(CH) if its*cliques*satisfy the*Helly*property, and it is hereditary*clique*-*Helly*(HCH) if H is*clique*-*Helly*for every induced subgraph H of G. ...##
###
Recognizing clique graphs of directed and rooted path graphs

1999
*
Discrete Applied Mathematics
*

We describe characterizations for the classes of

doi:10.1016/s0166-218x(99)00028-1
fatcat:uznrmhjw5zbqfogmnpf3m444q4
*clique**graphs*of directed and rooted path*graphs*. ... The characterizations lead to polynomial time algorithms for*recognizing**graphs*of these classes. 0 1999 Elsevier Science B. ...*Recognizing*if G is a*clique*-*Helly**graph*can be done in 0(n3m) steps [17]. Constructing G' from G requires O(n) steps. ...##
###
The Complexity of Helly-$B_{1}$ EPG Graph Recognition

2019
*
Discrete Mathematics & Theoretical Computer Science
*

Moreover, we show that the problem of

doi:10.23638/dmtcs-22-1-19
fatcat:estm7plbifdxthqvvtbpq2zwly
*recognizing**Helly*-$B_1$-EPG*graphs*is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate*graphs*. ... In this paper, we show that given a*graph*$G$ and an integer $k$, the problem of determining whether $G$ admits a $B_k$-EPG representation whose edge-intersections of paths satisfy the*Helly*property, ... Regarding the complexity of*recognizing*B k -EPG*graphs*, only the complexity of*recognizing*a few of these sub-classes of EPG*graphs*has been determined: B 0 -EPG*graphs*can be*recognized*in polynomial ...##
###
The Complexity of Helly-B_1 EPG Graph Recognition
[article]

2020
*
arXiv
*
pre-print

Moreover, we show that the problem of

arXiv:1906.11185v3
fatcat:4ucb4lehnnc7po3ciuxjenj22u
*recognizing**Helly*-B_1-EPG*graphs*is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate*graphs*. ... In this paper, we show that given a*graph*G and an integer k, the problem of determining whether G admits a B_k-EPG representation whose edge-intersections of paths satisfy the*Helly*property, so-called ... Regarding the complexity of*recognizing*B k -EPG*graphs*, only the complexity of*recognizing*a few of these sub-classes of EPG*graphs*has been determined: B 0 -EPG*graphs*can be*recognized*in polynomial ...##
###
Helly property, clique raphs, complementary graph classes, and sandwich problems

2008
*
Journal of the Brazilian Computer Society
*

A

doi:10.1007/bf03192558
fatcat:imrynj3dgzbihpe45tl5xn23hi
*graph*is*clique*-*Helly*when its family of*cliques*satisfies the*Helly*property. A*graph*is hereditary*clique*-*Helly*when all of its induced subgraphs are*clique*-*Helly*. ... We show that the sandwich problems for the*graph*classes:*clique*,*clique*-*Helly*, hereditary*clique*-*Helly*, and*clique*-*Helly*nonhereditary are all NP -complete. ... Clearly, from Theorems 2 and 3 one can also*recognize*in polynomial time whether a*graph*is*clique*-*Helly*nonhereditary. ...##
###
Helly property, clique graphs, complementary graph classes, and sandwich problems

2008
*
Journal of the Brazilian Computer Society
*

A

doi:10.1590/s0104-65002008000200004
fatcat:tzu2sfmskjdblpg4gqfs66xto4
*graph*is*clique*-*Helly*when its family of*cliques*satisfies the*Helly*property. A*graph*is hereditary*clique*-*Helly*when all of its induced subgraphs are*clique*-*Helly*. ... We show that the sandwich problems for the*graph*classes:*clique*,*clique*-*Helly*, hereditary*clique*-*Helly*, and*clique*-*Helly*nonhereditary are all NP -complete. ... Clearly, from Theorems 2 and 3 one can also*recognize*in polynomial time whether a*graph*is*clique*-*Helly*nonhereditary. ...##
###
On the clique operator
[chapter]

1998
*
Lecture Notes in Computer Science
*

Among all the better studied

doi:10.1007/bfb0054327
fatcat:racvmnrqpzhddbnp6y74fpnyua
*graph*operators, K seems to be the richest one and many questions regarding it remain open. In particular, it is not known whether*recognizing*a*clique**graph*is in P. ... The*clique*operator K maps a*graph*G into its*clique**graph*, which is the intersection*graph*of the (maximal)*cliques*of G. ... A*graph*is HeUy when the family of its*cliques*is*Helly*. We denote by 74 the class of*Helly**graphs*. A family ~r is conformal when the*cliques*of Jr2 are all members of ~'. ...##
###
On the generalized Helly property of hypergraphs, cliques, and bicliques
[article]

2022
*
arXiv
*
pre-print

In addition, we generalize to (p,q)-

arXiv:2201.12610v1
fatcat:auwnntvpinaobjzsq2j24h74yi
*clique*-*Helly**graphs*the characterization of p-*clique*-*Helly**graphs*in terms of expansions and give different characterizations of hereditary (p,q)-*clique*-*Helly**graphs*... A*graph*is (p,q)-*clique*-*Helly*if the family of its maximal*cliques*has the (p,q)-the*Helly*property and hereditary (p,q)-*clique*-*Helly*if each of its induced subgraphs is (p,q)-*clique*-*Helly*. ... The (p, q)-*clique*-*Helly*property of*graphs*In this section, we study the problems of characterizing and*recognizing*(p, q)-*clique*-*Helly**graphs*and hereditary (p, q)-*clique*-*Helly**graphs*. ...##
###
Recognizing clique graphs of directed edge path graphs

2003
*
Discrete Applied Mathematics
*

In this work, we show that the

doi:10.1016/s0166-218x(02)00203-2
fatcat:x2navd3fdvhlzcrm2nmokmnqte
*clique**graphs*of these*graphs*are exactly the two sections of the same kind of path families, and give a polynomial time recognition algorithm for them. ? ... Directed edge path*graphs*are the intersection*graphs*of directed paths in a directed tree, viewed as sets of edges. They were studied by Monma and Wei (J. Comb. ... Since*recognizing**clique*-*Helly**graphs*and DE*graphs*can be done in polynomial time [7, 9] , and the number of*cliques*of a duallyDE*graph*is also polynomial by Theorem 5, the entire procedure takes polynomial ...
« Previous

*Showing results 1 — 15 out of 286 results*