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Homogeneously representable interval graphs

1985
*
Discrete Mathematics
*

We characterize those

doi:10.1016/0012-365x(85)90049-4
fatcat:6vu2wvfzive2pmtiwiyjpiuuye
*interval**graphs*G with the property that, for every vertex u, there exists an*interval**represention*of G in which the*interval*representing 21 is the left-most (or right-most)*interval*... in the*representation*. 0012-365)3/85/$3.30 0 1985, Elsevier Science Publishers B.V. ... For example, the*graph*in Fig. 1 is a*homogeneously**representable**interval**graph*, but neither of the*graphs*in Fig. 2 is*homogeneously**representable*. ...##
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On Homogeneously Representable Interval Graphs

2015
*
National academy science letters
*

We determine all

doi:10.1007/s40009-015-0397-x
fatcat:e2ojbqz4sfckdd6pukap7bvcay
*graphs*whose line*graphs*(middle*graphs*, total*graphs*, respectively) are*homogeneously**representable**interval**graphs*. ... A*graph*G is called a*homogeneously**representable**interval**graph*(shortly, an HRI*graph*) if for every vertex v of G there exists an*interval**representation*of G in which the*interval*representing v is ... In the next two theorems we characterize all*graphs*G whose line*graphs*LðGÞ are*homogeneously**representable**interval**graphs*. ...##
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On the Recognition of Fuzzy Circular Interval Graphs
[article]

2011
*
arXiv
*
pre-print

Fuzzy circular

arXiv:1104.2251v1
fatcat:32pzpopln5esrcydycsn5iaqxm
*interval**graphs*are a generalization of proper circular arc*graphs*and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of claw-free*graphs*. ... In this paper, we provide a polynomial-time algorithm for recognizing such*graphs*, and more importantly for building a suitable*representation*. ... G is a fuzzy linear*interval**graph*if and only if G| (K 1 ,K 2 ) is a fuzzy linear*interval**graph*and, from a*representation*for G, one may build in O(n 2 )-time a*representation*for G| (K 1 ,K 2 ) , and ...##
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End vertices in interval graphs

1988
*
Discrete Applied Mathematics
*

We also present a short proof of a characterization of

doi:10.1016/0166-218x(88)90071-6
fatcat:wokmaa7mgjgupeoqmsdiqyfuky
*homogeneously**representable**interval**graphs*. < ... We characterize those vertices v in*interval**graphs*for which there is some*representation*of G where the*interval*corresponding to v is an end*interval*. ... It is clear that no*homogeneously**representable**interval**graph*contains either the S-path or the A-*graph*as induced subgraphs. ...##
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On sources in comparability graphs, with applications

1992
*
Discrete Mathematics
*

We characterize sources in comparability

doi:10.1016/0012-365x(92)90721-q
fatcat:nctlhvz7tjdtbcgubbfbkb7k7q
*graphs*and show that our result provides a unifying look at two recent results about*interval**graphs*. ... An orientation 0 of a*graph*G is obtained by assigning unique directions to its ... Theorem 1 implies the following characterization of the*homogeneously**representable**interval**graphs*. Corollary 1.2 (Skrien and Gimbel [6] ). ...##
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Page 4980 of Mathematical Reviews Vol. , Issue 86k
[page]

1986
*
Mathematical Reviews
*

The authors prove that an

*interval**graph*G is a*homogeneously**representable**interval**graph*if and only if ... An*interval**graph*G is said to be*homogeneously**representable*if for every vertex v in G there exists an*interval**representation*of G in which the*interval*representing v is an end*interval*. ...##
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Interval graphs and related topics

1985
*
Discrete Mathematics
*

Gimble,

doi:10.1016/0012-365x(85)90039-1
fatcat:3lkhvtmp3jdv5drohuptcyj3su
*Homogeneously**representable**interval**graphs*, Discrete Math. 55 (1985) (this issue). [ 111 M.H. ... Skrien and Gimble [lo] call an*interval**graph*G*homogeneously**representable*if for every vertex u there exists an*interval**representation*of G in which the*interval*representing n is the left-most (or ...##
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Page 1062 of Mathematical Reviews Vol. 42, Issue 5
[page]

1971
*
Mathematical Reviews
*

The

*graphs*G which admit intersection*representations*where the family F is a family of*intervals*in a linearly ordered set have been characterized by several authors. A. Tucker [Bull. Amer. Math. ... Conditions for pseudo L,(k)*graphs*to be*representation*of a*graph*@ by arcs in a*graph*H. Such a geometrizable. ...##
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Twin-width and Limits of Tractability of FO Model Checking on Geometric Graphs
[article]

2022
*
arXiv
*
pre-print

We also prove a similar excluded-subgraphs characterization for hereditary classes of

arXiv:2204.13742v1
fatcat:sipccgq3mjhhrahthommhl2f5i
*interval**graphs*with FO model checking in FPT, which concludes the line a research of*interval*classes with tractable ...*graph*classes, but much less understood on hereditary dense*graph*classes. ... The classes of*interval*and of*interval*-overlap*graphs*have FO*interval*-like*representations*. ...##
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Finding a smallest odd hole in a claw-free graph using global structure

2013
*
Discrete Applied Mathematics
*

In this paper we use this result to give an improved shortest-oddhole algorithm for claw-free

doi:10.1016/j.dam.2013.04.026
fatcat:omnzksiuvna2db7kftewnjkhlq
*graphs*by exploiting the structural relationship between line*graphs*and quasi-line*graphs*suggested by Chudnovsky ... and Seymour's structure theorem for quasi-line*graphs*. ... Accordingly, a circular*interval**graph*is a*graph*with a circular*interval**representation*, i.e. ...##
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Finding a smallest odd hole in a claw-free graph using global structure
[article]

2011
*
arXiv
*
pre-print

In this paper we use this result to give an improved shortest-odd-hole algorithm for claw-free

arXiv:1103.6222v2
fatcat:y4oa7m5f2fhuhkqqyknoiaumsi
*graphs*by exploiting the structural relationship between line*graphs*and quasi-line*graphs*suggested by Chudnovsky ... and Seymour's structure theorem for quasi-line*graphs*. ... Accordingly, a circular*interval**graph*is a*graph*with a circular*interval**representation*, i.e. ...##
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Page 45 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

An

*interval**graph*G is*homogeneously**representable*if for every vertex x of G, there exists an*interval**representation*of G with xX corresponding to an end*interval*. ... Tomaz Pisanski (YU-LJUB) 92a:05046 05C10 Olariu, Stephan (1-ODM) On the*homogeneous**representation*of*interval**graphs*. J.*Graph*Theory 15 (1991), no. 1, 65-80. ...##
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On the recognition of fuzzy circular interval graphs

2012
*
Discrete Mathematics
*

Fuzzy circular

doi:10.1016/j.disc.2011.12.029
fatcat:y3af6nzlprbkngbz4okzmmgeya
*interval**graphs*are a generalization of proper circular arc*graphs*and have been recently introduced by Chudnovsky and Seymour as a fundamental subclass of clawfree*graphs*. ... In this paper, we provide a polynomial time algorithm for recognizing such*graphs*, and more importantly for building a suitable model for these*graphs*. ... Therefore, we may associate with a CIG both a*representation*based on*intervals*and a*representation*based on arcs. Proper circular arc*graphs*have been studied extensively in the last decades. ...##
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On the interval number of special graphs

2004
*
Journal of Graph Theory
*

The

doi:10.1002/jgt.20005
fatcat:x5bxdefqujhq3b6zlgoqtkdqwe
*interval*number of a*graph*G is the least natural number t such that G is the intersection*graph*of sets, each of which is the union of at most t*intervals*, denoted by i (G ). ... We describe the extremal*graphs*for that inequality when d is even. For three special perfect*graph*classes we give bounds on the*interval*number in terms of the independence number. ... A*representation*is depth-two, if every point of the line is covered by at most two*intervals*. Theorem 1.2 [8] . If a*graph*G has a depth-two t*interval**representation*, then t ! dðeðGÞ þ 1Þ=vðGÞe. ...##
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Reasoning at the Right Time Granularity
[article]

2012
*
arXiv
*
pre-print

Continuous Time Bayesian Networks (CTBNs) avoid time-slicing in the

arXiv:1206.5260v1
fatcat:su2pglen65henhv6rvvge2tlaq
*representation*by modeling the system as evolving continuously over time. ... In this paper, we provide a new EP algorithm that utilizes a general cluster*graph*architecture where clusters contain distributions that can overlap in both space (set of variables) and time. ... Additional partitioning of I jk allows us to have a richer piecewise*homogeneous**representation*over the same*interval*. ...
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