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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

*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. ...

*The*author is deeply grateful to Grigori Olshanski for suggesting

*the*problem and many fruitful discussions. ...

##
###
The interval number of a planar graph is at most three

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. ...

##
###
Food Webs, Competition Graphs, and Habitat Formation

2011
*
Mathematical Modelling of Natural Phenomena
*

, determine trophic levels, dominant species, stability

doi:10.1051/mmnp/20116602
fatcat:dn4wqs2dnngv3k4cm2ztzm4ddm
*of**the*ecosystem, competition*graphs*,*interval**graphs*, and even confront problems that would appear to have logical answers that are as yet unsolved ...*The*first biology courses in high school and in college present*the*fundamental nature*of*a food web,*one*that is understandable by students at all levels. ... This*remarkable*empirical observation*of*Joel Cohen's [1] , that real-world competition*graphs*are usually*interval**graphs*, has led to a great deal*of*research*on**the*structure*of*competition*graphs*and ...##
###
The PIGs Full Monty – A Floor Show of Minimal Separators
[chapter]

2005
*
Lecture Notes in Computer Science
*

We show that

doi:10.1007/978-3-540-31856-9_43
fatcat:mrvgdp2fxrgmjiuj6iss4nkfdm
*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 ... This separator can occur at a*number**of*places in D. Definition 7. An occurrence*of*Ω in D is a maximal*interval*i ≤ j such that Ω is*of**one**of**the*types mentioned in Theorem 1.*Remark*6. ...##
###
On the unit interval number of a graph

1988
*
Discrete Applied Mathematics
*

This concept generahzes

doi:10.1016/0166-218x(88)90118-7
fatcat:5bwazx6oxjaupjf2w2qamjdytq
*the*notion*of*a unit*interval**graph*m*the*same way as*the*previously studted*Interval**number*generahzes*the*notion*of*an*interval**graph*We present*the*followmg results*on**the*umt ...*The*unit*Interval**number**of*a simple unduected*graph*G, denoted r,(G), IS*the*least nonnegatrve integer r for which we can assign to each vertex m G a collectIon*of*at most r closed umt*intervals**on**the*...*Graphs*with*interval**number*at most*one*are called*interval**graphs*. ...##
###
Split Domination In Interval-valued Fuzzy Graphs

2021
*
Asian Journal of Probability and Statistics
*

We investigated and study

doi:10.9734/ajpas/2021/v15i430360
fatcat:tfzosbo7lfhrhd33pur2leogoe
*the*relationship*of*γs with other known parameters in*interval*-valued fuzzy*graph*. Finally we calculated γs(G) for some standard*interval*valued fuzzy*graphs*. ... Aims / Objectives: In this paper, we introduced and investigated*the*concept*of*split domination in*interval*-valued fuzzy*graph*and denoted by γs. We obtained many results related to γs. ... are*intervals**of**numbers*instead*of**the**numbers*. ...##
###
On powers of m-trapezoid graphs

1995
*
Discrete Applied Mathematics
*

First a new class

doi:10.1016/0166-218x(95)00062-v
fatcat:g4ig7xejpngpdobmg4vzj2tpve
*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. ...*The*main result*of*this paper is that if GL-' is an m-trapezoid*graph*then Gk is also an m-trapezoid*graph*. ... Acknowledgements*The*result*of*this paper forms part*of*my dissertation written under*the*supervision*of*Dr. Erich Prisner. ...##
###
On the benchmark instances for the Bin Packing with Conflicts
[article]

2017
*
arXiv
*
pre-print

In this paper we prove that

arXiv:1706.03526v3
fatcat:ntxvmvxxb5ekbouwniicwkdnqy
*the**graphs*generated in this way are not arbitrary but threshold*ones*. ... Many authors, mainly in*the*context*of**the*Bin Packing Problem with Conflicts, used*the*random*graph*generator proposed in "Heuristics and lower bounds for*the*bin packing problem with conflicts" [M. ... We*remark*that, as far as we know, no tests*on*instances*of*BP P C with arbitrary*interval*conflict*graphs*were performed in*the*literature. ...##
###
Approximate Capacity of Index Coding for Some Classes of Graphs
[article]

2016
*
arXiv
*
pre-print

For a class

arXiv:1602.02422v1
fatcat:43v75enrcfehzh6paevkgryfby
*of**graphs*for which*the*Ramsey*number*R(i,j) is upper bounded by ci^aj^b, for some constants a,b, and c, it is shown that*the*clique covering scheme approximates*the*broadcast rate*of*every ... Using this theorem and some*graph*theoretic arguments, it is demonstrated that*the*broadcast rate*of*planar*graphs*, line*graphs*and fuzzy circular*interval**graphs*is approximated by*the*clique covering ... Let P be*the*class*of*planar*graphs*. As P contains all edgeless*graphs*,*the*Ramsey*number*for this class is completely determined by*Remark*1 and*the*following. [15] ). ...##
###
Constructing colorings for diagrams

1994
*
Discrete Applied Mathematics
*

In particular we investigate

doi:10.1016/0166-218x(94)90096-5
fatcat:t4oz2qulp5c4rnehtdrrz5djnu
*the*chromatic*number**of*diagrams*of*special classes*of*posets such as semi-orders, series-parallel orders, N-free orders and*interval*orders. Elsevier Science B.V. ... We discuss bounds for and algorithmic aspects*of**the*chromatic*number**of*diagrams. ... Triangle-free*graphs*, and hence diagrams, admit colorings with O(&/log log n) colors. Proof. We combine two bounds*on**the*size*of*independent sets in a triangle-free*graph*. ...##
###
Certain Types of Interval-Valued Fuzzy Graphs

2013
*
Journal of Applied Mathematics
*

We also describe

doi:10.1155/2013/857070
fatcat:tdicdtd35vdnhppk7qwnohx7vi
*the*relationship between intuitionistic fuzzy*graphs*and*interval*-valued fuzzy*graphs*. ... We propose certain types*of**interval*-valued fuzzy*graphs*including balanced*interval*-valued fuzzy*graphs*, neighbourly irregular*interval*-valued fuzzy*graphs*, neighbourly total irregular*interval*-valued ... Acknowledgments*The*authors are thankful to*the*referees for their valuable comments.*The*authors are also thankful to Professor Syed Mansoor Sarwar and Dr. ...##
###
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 persistent-*interval*for its vertex x if*the*spectrum*of*x is an*interval**of*integers beginning from*the*color 1. ... For an arbitrary*graph*G and any ϕ ∈ α(G), we denote by f G,i (ϕ)(f G,pi (ϕ))*the**number**of*vertices*of**the**graph*G for which ϕ is*interval*(persistent-*interval*). ...##
###
Page 3172 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

This concept generalizes

*the*notion*of*a unit*interval**graph*in*the*same way as*the*previously studied*interval**number*generalizes*the*notion*of*an*interval**graph*. ... No natural*one*-to-*one*correspondence between*the*two kinds*of*maps is presented. Jozef Siran (CS-STU) 90f:05072 05C35 Andreae, Thomas (D-HAMB)*On**the*unit*interval**number**of*a*graph*. Discrete Appl. ...##
###
A new and efficient method for elementary fuzzy arithmetic operations on pseudo-geometric fuzzy numbers

2016
*
Journal of Fuzzy Set Valued Analysis
*

In this regard, this paper provide a new method regarding

doi:10.5899/2016/jfsva-00303
fatcat:2slumemgorcujariyi33on5ukm
*the*effective practical computation*of*elementary fuzzy arithmetic operations*on*pseudo-geometric fuzzy*numbers*. ... extension principle (in*the*domain*of**the*membership function) or*the**interval*arithmetics (in*the*domain*of*α -cuts). ... Figure 4 : 4 Figure 4:*The**graph**of*addition TA operation*on*pseudo-trapezoidal fuzzy*numbers*. Figure 5 : 5 Figure 5:*The**graph**of*multiplication TA operation*on*pseudo-trapezoidal fuzzy*numbers*. ...##
###
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). ... We consider*the*meeting*graph**of*F introduced by Eisenbeis, Lelait and Marmol. Proceedings*of**the*Fifth Workshop*on*Compilers for Parallel Computers, Malaga, June 1995, pp. 502-515. ...*The*support*of**the*CNR*of*Italy is gratefully acknowledged. S. Lelait is currently supported by a Lise-Meitner Stipendium from*the*Austrian Ministry*of*Science (FWF). ...
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