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Semifinite harmonic functions on the Gnedin-Kingman graph [article]

Nikita Safonkin
2021 arXiv   pre-print
The paper contains a detailed announcement of results concerning the classification of indecomposable semifinite harmonic functions on the Gnedin-Kingman graph.  ...  We study the Gnedin-Kingman graph, which corresponds to Pieri's rule for the monomial basis {M_λ} in the algebra QSym of quasisymmetric functions.  ...  Remark 3.7. The infinite composition GK u does not depend on the lengths of the intervals, but depends on their relative position.  ... 
arXiv:2103.02257v2 fatcat:z6a6gixslzb77exhtw7lfm2mqe

On powers of m-trapezoid graphs

Carsten Flotow
1995 Discrete Applied Mathematics  
First a new class of graphs is introduced: m-trapezoid graphs are the intersection graphs of m-trapezoids, where an m-trapezoid is given by m + 1 intervals on m + 1 parallel lines.  ...  This theorem has some interesting corollaries concerning interval graphs, trapezoid graphs and cocomparability graphs: If A is either of these classes, then G'-' E A implies d E A.  ...  I also thank Andreas Parra for the tea-time at which he had told me about trapezoid graphs.  ... 
doi:10.1016/0166-218x(95)00062-v fatcat:g4ig7xejpngpdobmg4vzj2tpve

Linear time recognition of P4-indifference graphs

Michel Habib, Christophe Paul, Laurent Viennot
2001 Discrete Mathematics & Theoretical Computer Science  
International audience A graph is a P4-indifference graph if it admits an ordering < on its vertices such that every chordless path with vertices a, b, c, d and edges ab, bc, cd has a  ...  We can remark that this graph contains modules ( a a ¼ and d d ¼ ).  ...  Notice that the previous remarks imply that x and y are vertices of some P 4 in each of the three situations of Theorem 3. Moreover any two consecutive vertices of some P 4 are in relation by .  ... 
doi:10.46298/dmtcs.269 fatcat:cfyilyrhg5bdtazqw6uddohbcy

Closed orders and closed graphs [article]

Marilena Crupi
2015 arXiv   pre-print
A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.  ...  The class of closed graphs by a linear ordering on their sets of vertices is investigated.  ...  on closed graphs [2] via some properties of proper interval graphs.  ... 
arXiv:1509.06554v1 fatcat:x6l2kkovwvg3xjx4ev3yvph2vi

The graph isomorphism problem on geometric graphs

Ryuhei Uehara
2014 Discrete Mathematics & Theoretical Computer Science  
Sometimes the GI problem becomes polynomial time solvable when we add some restrictions on some graph classes.  ...  In this paper, we survey the computational complexity of the problem on some graph classes that have geometric characterizations.  ...  In 1970s, some efficient algorithms were developed for the GI problem on basic graph classes, which include planar graphs (Hopcroft and Tarjan (1974) ), interval graphs (Booth and Lueker (1976) ).  ... 
doi:10.46298/dmtcs.2076 fatcat:opywyghknffdpgho5jaxuycgwm

A note on path domination

Liliana Alcón
2016 Discussiones Mathematicae Graph Theory  
We thereby obtained new characterizations of standard graph classes like chordal, interval and superfragile graphs.  ...  We succeeded in characterizing those graphs in which every uv-walk of one particular kind dominates every uv-walk of other specific kind.  ...  Acknowledgements The author is grateful to Boštjan Brešar for the fruitful comments on a first draft of this paper, and to the anonymous referees whose suggestions greatly improved the manuscript.  ... 
doi:10.7151/dmgt.1917 fatcat:6k3b2xgyxjfclk4k2jjqsbnr64

Counting Kernels in Directed Graphs with Arbitrary Orientations [article]

Bruno Jartoux
2022 arXiv   pre-print
By contrast, we count the kernels of a fuzzy circular interval graph in polynomial time, regardless of its edge orientations, and return a kernel when one exists.  ...  We also consider kernels on cographs, where we establish NP-hardness in general but linear running times on the subclass of threshold graphs.  ...  Interval graphs and interval digraphs. There are some results on kernel problems in interval digraphs [FHJ21] .  ... 
arXiv:2202.04476v2 fatcat:gf4gix2z2vclhivbftq2murn7u

Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs [article]

R.R. Kamalian
2012 arXiv   pre-print
For graphs G from some classes of graphs, we obtain estimates for the possible number of vertices for which a proper edge t-coloring of G can be interval or persistent-interval.  ...  A proper edge t-coloring of a graph G is interval for its vertex x if the spectrum of x is an interval of integers.  ...  Remark 4 Some sufficient conditions for existence of an interval coloring of a (3, 4)biregular bipartite graph were obtained in [ 2, 5, 20]. Case 14 2 j 0 ∈ 0 [1, k − 1].  ... 
arXiv:1205.0131v1 fatcat:jz5i3ltzbjabhp2gmaekbjim3y

Completion of the mixed unit interval graphs hierarchy [article]

Alexandre Talon, Jan Kratochvíl
2017 arXiv   pre-print
We describe the missing class of the hierarchy of mixed unit interval graphs, generated by the intersection graphs of closed, open and one type of half-open intervals of the real line.  ...  This class lies strictly between unit interval graphs and mixed unit interval graphs.  ...  The overall idea of the proof is the following: if, in the neighborhood of an open-closed interval, one of the mentioned intervals is missing, then we can shift some intervals and close the left end of  ... 
arXiv:1412.0540v4 fatcat:jy7padpelndpdl3cjzg5raxvdq

The interval number of a planar graph is at most three

Guillaume Guégan, Kolja Knauer, Jonathan Rollin, Torsten Ueckerdt
2021 Journal of combinatorial theory. Series B (Print)  
The interval number of a graph G is the minimum k such that one can assign to each vertex of G a union of k intervals on the real line, such that G is the intersection graph of these sets, i.e., two vertices  ...  Scheinerman and West (1983) [14] proved that the interval number of any planar graph is at most 3. However the original proof has a flaw. We give a different and shorter proof of this result.  ...  Moreover, we thank Ed Scheinerman and Douglas West for their helpful comments on an earlier version of this manuscript and for providing us a copy of Ed's PhD thesis.  ... 
doi:10.1016/j.jctb.2020.07.006 fatcat:ij3tcp3dpzfevdor4esqs3qaqq

On a graph-theoretical model for cyclic register allocation

D. de Werra, Ch. Eisenbeis, S. Lelait, B. Marmol
1999 Discrete Applied Mathematics  
It can be formulated as a coloring problem in a circular arc graph (intersection graph of a family F of intervals on a circle).  ...  Furthermore some properties of the chromatic number for periodic circular arc graphs are derived. ? Werra) 0166-218X/99/$ -see front matter ? 1999 Elsevier Science B.V. All rights reserved.  ...  SinceĜ is the adjoint of some graph G, we know from the above remarks that the split S(Ĝ) ofĜ consists of node disjoint complete bipartite graphs.  ... 
doi:10.1016/s0166-218x(99)00105-5 fatcat:brjytyh6frcffgd6dwxjh2potu

Food Webs, Competition Graphs, and Habitat Formation

M. Cozzens
2011 Mathematical Modelling of Natural Phenomena  
, interval graphs, and even confront problems that would appear to have logical answers that are as yet unsolved.  ...  One interesting example of a discrete mathematical model used in biology is a food web.  ...  Show the interval representation. b. Give some examples of graphs that are not interval graphs. Figure 7 : 7 , cannot be represented by intervals on the real line.  ... 
doi:10.1051/mmnp/20116602 fatcat:dn4wqs2dnngv3k4cm2ztzm4ddm

Limits of interval orders and semiorders [article]

Svante Janson
2011 arXiv   pre-print
In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed subintervals of [0,1], and we define a subset of such measures that yield a  ...  We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders.  ...  P is a semiorder if and only if Ψ(P ) is a unit interval graph (a.k.a. indifference graph); moreover, every unit interval graph is Ψ(P ) for some semiorder P [9, Theorem 3.2].  ... 
arXiv:1104.1264v1 fatcat:mpzaqgx4dbfgpd4q36ghlncbne

Closed orders and closed graphs

Marilena Crupi
2016 Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica  
A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.  ...  The class of closed graphs by a linear ordering on their sets of vertices is investigated.  ...  Closed graphs via proper interval graphs In this Section, we discuss a recent result on closed graphs [2] via some properties of proper interval graphs.  ... 
doi:10.1515/auom-2016-0034 fatcat:3nbi57x7c5h5hl3middyejc3zu

The PIGs Full Monty – A Floor Show of Minimal Separators [chapter]

Gerard Jennhwa Chang, Antonius J. J. Kloks, Jiping Liu, Sheng-Lung Peng
2005 Lecture Notes in Computer Science  
We show that the recognition problem of probe interval graphs, i.e., probe graphs of the class of interval graphs, is in P.  ...  Given a class of graphs G, a graph G is a probe graph of G if its vertices can be partitioned into two sets P (the probes) and N (nonprobes), where N is an independent set, such that G can be embedded  ...  Concluding remarks In this paper we presented the first polynomial time recognition algorithm for unpartitioned probe interval graphs.  ... 
doi:10.1007/978-3-540-31856-9_43 fatcat:mrvgdp2fxrgmjiuj6iss4nkfdm
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