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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.  ...  The author is deeply grateful to Grigori Olshanski for suggesting the problem and many fruitful discussions.  ... 
arXiv:2103.02257v2 fatcat:z6a6gixslzb77exhtw7lfm2mqe

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

Food Webs, Competition Graphs, and Habitat Formation

M. Cozzens
2011 Mathematical Modelling of Natural Phenomena  
, determine trophic levels, dominant species, stability 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  ... 
doi:10.1051/mmnp/20116602 fatcat:dn4wqs2dnngv3k4cm2ztzm4ddm

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

On the unit interval number of a graph

Thomas Andreae
1988 Discrete Applied Mathematics  
This concept generahzes 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.  ... 
doi:10.1016/0166-218x(88)90118-7 fatcat:5bwazx6oxjaupjf2w2qamjdytq

Split Domination In Interval-valued Fuzzy Graphs

Nojood A. AL-Khadari, Mahiuob M. Q. Shubatah
2021 Asian Journal of Probability and Statistics  
We investigated and study 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.  ... 
doi:10.9734/ajpas/2021/v15i430360 fatcat:tfzosbo7lfhrhd33pur2leogoe

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.  ...  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.  ... 
doi:10.1016/0166-218x(95)00062-v fatcat:g4ig7xejpngpdobmg4vzj2tpve

On the benchmark instances for the Bin Packing with Conflicts [article]

Tiziano Bacci, Sara Nicoloso
2017 arXiv   pre-print
In this paper we prove that 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.  ... 
arXiv:1706.03526v3 fatcat:ntxvmvxxb5ekbouwniicwkdnqy

Approximate Capacity of Index Coding for Some Classes of Graphs [article]

Fatemeh Arbabjolfaei, Young-Han Kim
2016 arXiv   pre-print
For a class 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] ).  ... 
arXiv:1602.02422v1 fatcat:43v75enrcfehzh6paevkgryfby

Constructing colorings for diagrams

Stefan Felsner, Jens Gustedt, Michel Morvan, Jean-Xavier Rampon
1994 Discrete Applied Mathematics  
In particular we investigate 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.  ... 
doi:10.1016/0166-218x(94)90096-5 fatcat:t4oz2qulp5c4rnehtdrrz5djnu

Certain Types of Interval-Valued Fuzzy Graphs

Muhammad Akram, Noura Omair Alshehri, Wieslaw A. Dudek
2013 Journal of Applied Mathematics  
We also describe 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.  ... 
doi:10.1155/2013/857070 fatcat:tdicdtd35vdnhppk7qwnohx7vi

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 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).  ... 
arXiv:1205.0131v1 fatcat:jz5i3ltzbjabhp2gmaekbjim3y

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

Fazlollah Abbasi, Saeid Abbasbandy, Juan J. Nieto
2016 Journal of Fuzzy Set Valued Analysis  
In this regard, this paper provide a new method regarding 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.  ... 
doi:10.5899/2016/jfsva-00303 fatcat:2slumemgorcujariyi33on5ukm

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).  ...  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).  ... 
doi:10.1016/s0166-218x(99)00105-5 fatcat:brjytyh6frcffgd6dwxjh2potu
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