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

2021
*
arXiv
*
pre-print

The paper contains a detailed announcement of results concerning the classification of indecomposable semifinite harmonic functions

arXiv:2103.02257v2
fatcat:z6a6gixslzb77exhtw7lfm2mqe
*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. ...##
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On powers of m-trapezoid graphs

1995
*
Discrete Applied Mathematics
*

First a new class of

doi:10.1016/0166-218x(95)00062-v
fatcat:g4ig7xejpngpdobmg4vzj2tpve
*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*. ...##
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Linear time recognition of P4-indifference graphs

2001
*
Discrete Mathematics & Theoretical Computer Science
*

International audience A

doi:10.46298/dmtcs.269
fatcat:cfyilyrhg5bdtazqw6uddohbcy
*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 . ...##
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Closed orders and closed graphs
[article]

2015
*
arXiv
*
pre-print

A recent characterization of such a class of

arXiv:1509.06554v1
fatcat:x6l2kkovwvg3xjx4ev3yvph2vi
*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*. ...##
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The graph isomorphism problem on geometric graphs

2014
*
Discrete Mathematics & Theoretical Computer Science
*

Sometimes the GI problem becomes polynomial time solvable when we add

doi:10.46298/dmtcs.2076
fatcat:opywyghknffdpgho5jaxuycgwm
*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) ). ...##
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A note on path domination

2016
*
Discussiones Mathematicae Graph Theory
*

We thereby obtained new characterizations of standard

doi:10.7151/dmgt.1917
fatcat:6k3b2xgyxjfclk4k2jjqsbnr64
*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. ...##
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Counting Kernels in Directed Graphs with Arbitrary Orientations
[article]

2022
*
arXiv
*
pre-print

By contrast, we count the kernels of a fuzzy circular

arXiv:2202.04476v2
fatcat:gf4gix2z2vclhivbftq2murn7u
*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] . ...##
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Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs
[article]

2012
*
arXiv
*
pre-print

For

arXiv:1205.0131v1
fatcat:jz5i3ltzbjabhp2gmaekbjim3y
*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]. ...##
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Completion of the mixed unit interval graphs hierarchy
[article]

2017
*
arXiv
*
pre-print

We describe the missing class of the hierarchy of mixed unit

arXiv:1412.0540v4
fatcat:jy7padpelndpdl3cjzg5raxvdq
*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 ...##
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The interval number of a planar graph is at most three

2021
*
Journal of combinatorial theory. Series B (Print)
*

The

doi:10.1016/j.jctb.2020.07.006
fatcat:ij3tcp3dpzfevdor4esqs3qaqq
*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. ...##
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On a graph-theoretical model for cyclic register allocation

1999
*
Discrete Applied Mathematics
*

It can be formulated as a coloring problem in a circular arc

doi:10.1016/s0166-218x(99)00105-5
fatcat:brjytyh6frcffgd6dwxjh2potu
*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*. ...##
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Food Webs, Competition Graphs, and Habitat Formation

2011
*
Mathematical Modelling of Natural Phenomena
*

,

doi:10.1051/mmnp/20116602
fatcat:dn4wqs2dnngv3k4cm2ztzm4ddm
*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. ...##
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Limits of interval orders and semiorders
[article]

2011
*
arXiv
*
pre-print

In the

arXiv:1104.1264v1
fatcat:mpzaqgx4dbfgpd4q36ghlncbne
*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]. ...##
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Closed orders and closed graphs

2016
*
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
*

A recent characterization of such a class of

doi:10.1515/auom-2016-0034
fatcat:3nbi57x7c5h5hl3middyejc3zu
*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*. ...##
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The PIGs Full Monty – A Floor Show of Minimal Separators
[chapter]

2005
*
Lecture Notes in Computer Science
*

We show that the recognition problem of probe

doi:10.1007/978-3-540-31856-9_43
fatcat:mrvgdp2fxrgmjiuj6iss4nkfdm
*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*. ...
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