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Algorithms for some intersection graphs
[chapter]

1981
*
Lecture Notes in Computer Science
*

Several

doi:10.1007/3-540-10704-5_15
fatcat:xzfteaeh5bavpj2bibjkserhzq
*intersection**graphs*such as curves-in-the-plane*graphs*, circular-arc*graphs*, chordal*graphs*and interval*graphs*are reviewed, especially on their recognition*algorithms*. ... In this connection*graph*realization problem is mentioned. ... Trivially, any*graph*is an*intersection**graph*on*some*appropriate model M [i] . ...##
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A proof of Pieri's formula using the generalized Schensted insertion algorithm for rc-graphs
[article]

2000
*
arXiv
*
pre-print

We provide a generalization of the Schensted insertion

arXiv:math/0010109v2
fatcat:icxqzkxeobd4xlxgs3vzhqzbja
*algorithm**for*rc-*graphs*of Bergeron and Billey. The new*algorithm*is used to give a new proof of Pieri's formula. ... This*algorithm*will take the*graph*, which was rectified upto the row ℓ, and remove*some**intersections*to produce an rc-*graph*of the original permutation w.*Algorithm*2. ... Now the result of*algorithm*2 will be a*graph*with the permutation w by Lemma 3.3, with exactly l(w)*intersections*. Therefore it will be an rc-*graph**for*w. ...##
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Algorithms for clique-independent sets on subclasses of circular-arc graphs

2006
*
Discrete Applied Mathematics
*

Also, we apply the

doi:10.1016/j.dam.2006.03.022
fatcat:eab6d2a6rnf7dibcduc4dbqqni
*algorithms*to the special case of an HCA*graph*. The complexity of the proposed*algorithm**for*the cardinality problem in HCA*graphs*is O(n). ... A circular-arc*graph*is the*intersection**graph*of arcs on a circle. A Helly circular-arc*graph*is a circular-arc*graph*admitting a model whose arcs satisfy the Helly property. ... The following are*some*classes of*graphs*admitting polynomial time*algorithms**for*the problems of determining a maximum clique-independent set: strongly chordal*graphs*[5, 14] ; chordal*graphs*with bounded ...##
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Independence and Coloring Problems on Intersection Graphs of Disks
[chapter]

2006
*
Lecture Notes in Computer Science
*

This chapter surveys on-line and approximation

doi:10.1007/11671541_5
fatcat:q7gquet6kraljam3wcoklhz6zm
*algorithms**for*the maximum independent set and coloring problems on*intersection**graphs*of disks. ... It includes a more detailed treatment of recent upper and lower bounds on the competitive ratio of on-line*algorithms**for*coloring such*graphs*. ... Observe that several of the presented results*for*disk*graphs*hold analogously*for**intersection**graphs*of squares and*for**intersection**graphs*of axis-aligned squares. ...##
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On cliques of Helly Circular-arc Graphs

2008
*
Electronic Notes in Discrete Mathematics
*

This gives a linear-time

doi:10.1016/j.endm.2008.01.020
fatcat:xzcp3yclwfhftnrhtmca7zeshm
*algorithm*to find a proper Helly model*for*the clique*graph*of a Helly circular-arc*graph*. ... This yields the first polynomial (linear) time recognition*algorithm**for*the clique*graphs*of Helly circular-arc*graphs*. ... The clique*graph*K(G) of G is the*intersection**graph*of its cliques. A*graph*is a clique*graph*if it is isomorphic to K(G)*for**some**graph*G [5, 8] . ...##
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Densest k-Subgraph Approximation on Intersection Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

This concept allows us to derive constant factor approximation

doi:10.1007/978-3-642-18318-8_8
fatcat:bkgw4vghebc7lhyizcmog7xlfi
*algorithms**for*DS-k on many*intersection**graph*classes, such as chordal*graphs*, circular-arc*graphs*, claw-free*graphs*, line*graphs*of -hypergraphs ... We study approximation solutions*for*the densest k-subgraph problem (DS-k) on several classes of*intersection**graphs*. ... It is unlikely that there exists a PTAS*for*general*graphs*[?].*For**some*special*graph*classes and special values of k, better*algorithms*are known [?,?,?]. ...##
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Complexity results on graphs with few cliques

2007
*
Discrete Mathematics & Theoretical Computer Science
*

Several classes of

doi:10.46298/dmtcs.387
fatcat:zd566nxpufhvrfaej6urs5l7nm
*graphs*which have few cliques are discussed, and the complexity of*some*partitioning and covering problems are determined*for*the class of all*graphs*which have fewer cliques than a ... On any such class of*graphs*,*some*problems that are NP-complete on general*graphs*, such as the maximum clique problem and the maximum weighted clique problem, admit polynomial time*algorithms*. ... Note that polynomial time*algorithms**for**graphs*with few cliques can be made robust (that is, when given input not in the class of*graphs*the*algorithm*is designed*for*, the*algorithm*either rejects or ...##
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Efficiently Testing $$T$$ -Interval Connectivity in Dynamic Graphs
[chapter]

2015
*
Lecture Notes in Computer Science
*

We show that Ω(δ) such operations are required to solve both problems, and we present optimal O(δ) online

doi:10.1007/978-3-319-18173-8_6
fatcat:cgspf3pqrnffdfzojpyvz5kyoi
*algorithms**for*both problems. ... We assume that the changes between two consecutive*graphs*are arbitrary, and that two operations, binary*intersection*and connectivity testing, are available to solve the problems. ... . , G ℓ [δ − ℓ + 1],*for**some*k + 1 ≤ ℓ ≤ 2k. ...##
###
Efficiently Testing T-Interval Connectivity in Dynamic Graphs
[article]

2017
*
arXiv
*
pre-print

We show that Ω(δ) such operations are required to solve both problems, and we present optimal O(δ) online

arXiv:1502.00089v3
fatcat:jvqzcusb6jal7nfhzn2sne4oiu
*algorithms**for*both problems. ... We assume that the changes between two consecutive*graphs*are arbitrary, and that two operations, binary*intersection*and connectivity testing, are available to solve the problems. ... . , G ℓ [δ − ℓ + 1],*for**some*k + 1 ≤ ℓ ≤ 2k. ...##
###
The graph isomorphism problem on geometric graphs

2014
*
Discrete Mathematics & Theoretical Computer Science
*

We also show that the GI problem is as hard as the problem on general

doi:10.46298/dmtcs.2076
fatcat:opywyghknffdpgho5jaxuycgwm
*graphs*even*for*grid unit*intersection**graphs*on a torus, that partially solves an open problem. ... Sometimes the GI problem becomes polynomial time solvable when we add*some*restrictions on*some**graph*classes. ... Since the Reingold's log-space*algorithm**for*undirected connectivity (Reingold (2008) ),*some*log-space*algorithms**for*planar*graphs*(Datta et al. (2009) ) and interval*graphs*(Köbler et al. (2011) ...##
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An E log E Line Crossing Algorithm for Levelled Graphs
[chapter]

1999
*
Lecture Notes in Computer Science
*

This paper describes an

doi:10.1007/3-540-46648-7_6
fatcat:bfulii6r3jf3tltq2yzawd2xw4
*algorithm**for*leveled*graphs*, based on the classification of edges that is O(e log e) where e is the number of edges. ... It is also a performance bottleneck*for*Sugiyama-style layout*algorithms*. ... We have discovered by experience that counting line*intersections*is a performance bottleneck*for*the entire*algorithm**for*large*graphs*. ...##
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The topological drawing of a graph: Construction methods

2013
*
Automation and remote control
*

This paper considers construction

doi:10.1134/s0005117913090063
fatcat:rdlqyvukpzex3a7oivwrgq54se
*algorithms**for*the topological 2-D drawing of a*graph*. These*algorithms*allow to store, describe and modify the existing information on the drawing of a*graph*. ... Finally, we introduce necessary notions and structures to solve the problem of the topological 2-D drawing of a*graph*. ... Lee's*algorithm*belongs to metrical methods, since connections are considered in*some*subspace of R 2 with the Euclidean metric. ...##
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Optimization problems in multiple subtree graphs

2011
*
Discrete Applied Mathematics
*

We consider various optimization problems in t-subtree

doi:10.1016/j.dam.2010.03.010
fatcat:5ztkkwoibve3dbxfcqkmmg2lji
*graphs*, the*intersection**graphs*of t-subtrees, where a t-subtree is the union of t disjoint subtrees of*some*tree. ... We present approximation*algorithms**for*the Maximum Independent Set, Minimum Coloring, Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique problems in t-subtree*graphs*. ...*graphs*by Martin), but also*for*the numerous hallway discussions with him about life and academia. ...##
###
Optimization Problems in Multiple Subtree Graphs
[chapter]

2010
*
Lecture Notes in Computer Science
*

We consider various optimization problems in t-subtree

doi:10.1007/978-3-642-12450-1_18
fatcat:ocs76hoo2jelvmkuvnmtqhxfoy
*graphs*, the*intersection**graphs*of t-subtrees, where a t-subtree is the union of t disjoint subtrees of*some*tree. ... We present approximation*algorithms**for*the Maximum Independent Set, Minimum Coloring, Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique problems in t-subtree*graphs*. ...*graphs*by Martin), but also*for*the numerous hallway discussions with him about life and academia. ...##
###
The clique-separator graph for chordal graphs

2009
*
Discrete Applied Mathematics
*

We present an

doi:10.1016/j.dam.2009.02.006
fatcat:fmi7qczjujah5owwzxaym33eta
*algorithm*that constructs the clique-separator*graph*of a chordal*graph*in O(n 3 ) time and of an interval*graph*in O(n 2 ) time, where n is the number of vertices in the*graph*. ... We present structural properties of the clique-separator*graph*and additional properties when the chordal*graph*is an interval*graph*, proper interval*graph*, or split*graph*. ... Then*Intersect*(N) ⊆*Intersect*(S) and we must show that*Intersect*(N) ⊂*Intersect*(S). Since S N, it follows that N is in*some*connected component of G − P reds(S). ...
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