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Homogeneously representable interval graphs
1985
Discrete Mathematics
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We characterize those 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. ...
doi:10.1016/0012-365x(85)90049-4
fatcat:6vu2wvfzive2pmtiwiyjpiuuye
On Homogeneously Representable Interval Graphs
2015
National academy science letters
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We determine all 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. ...
doi:10.1007/s40009-015-0397-x
fatcat:e2ojbqz4sfckdd6pukap7bvcay
On the Recognition of Fuzzy Circular Interval Graphs
[article]
2011
arXiv
pre-print
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Fuzzy circular 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 ...
arXiv:1104.2251v1
fatcat:32pzpopln5esrcydycsn5iaqxm
End vertices in interval graphs
1988
Discrete Applied Mathematics
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We also present a short proof of a characterization of 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. ...
doi:10.1016/0166-218x(88)90071-6
fatcat:wokmaa7mgjgupeoqmsdiqyfuky
On sources in comparability graphs, with applications
1992
Discrete Mathematics
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We characterize sources in comparability 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] ). ...
doi:10.1016/0012-365x(92)90721-q
fatcat:nctlhvz7tjdtbcgubbfbkb7k7q
Page 4980 of Mathematical Reviews Vol. , Issue 86k
[page]
1986
Mathematical Reviews
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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. ...
Interval graphs and related topics
1985
Discrete Mathematics
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Gimble, 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 ...
doi:10.1016/0012-365x(85)90039-1
fatcat:3lkhvtmp3jdv5drohuptcyj3su
Page 1062 of Mathematical Reviews Vol. 42, Issue 5
[page]
1971
Mathematical Reviews
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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. ...
Twin-width and Limits of Tractability of FO Model Checking on Geometric Graphs
[article]
2022
arXiv
pre-print
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We also prove a similar excluded-subgraphs characterization for hereditary classes of 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. ...
arXiv:2204.13742v1
fatcat:sipccgq3mjhhrahthommhl2f5i
Finding a smallest odd hole in a claw-free graph using global structure
2013
Discrete Applied Mathematics
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In this paper we use this result to give an improved shortest-oddhole algorithm for claw-free 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. ...
doi:10.1016/j.dam.2013.04.026
fatcat:omnzksiuvna2db7kftewnjkhlq
Finding a smallest odd hole in a claw-free graph using global structure
[article]
2011
arXiv
pre-print
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In this paper we use this result to give an improved shortest-odd-hole algorithm for claw-free 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. ...
arXiv:1103.6222v2
fatcat:y4oa7m5f2fhuhkqqyknoiaumsi
Page 45 of Mathematical Reviews Vol. , Issue 92a
[page]
1992
Mathematical Reviews
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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. ...
On the recognition of fuzzy circular interval graphs
2012
Discrete Mathematics
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Fuzzy circular 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. ...
doi:10.1016/j.disc.2011.12.029
fatcat:y3af6nzlprbkngbz4okzmmgeya
On the interval number of special graphs
2004
Journal of Graph Theory
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The 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. ...
doi:10.1002/jgt.20005
fatcat:x5bxdefqujhq3b6zlgoqtkdqwe
Reasoning at the Right Time Granularity
[article]
2012
arXiv
pre-print
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Continuous Time Bayesian Networks (CTBNs) avoid time-slicing in the 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. ...
arXiv:1206.5260v1
fatcat:su2pglen65henhv6rvvge2tlaq
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