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A metric graph satisfying [...] w 4 1 = 1 w 4 1 = 1 that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 dim ( W 4 1 ) = 1

Marc Coppens (2016)

Open Mathematics

For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1 w 4 1 = 1 such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

A metric on a system of ordered sets

Alfonz Haviar, Pavel Klenovčan (1996)

Mathematica Bohemica

In [3] a metric on a system of isomorphism classes of ordered sets was defined. In this paper we define another metric on the same system and investigate some of its properties. Our approach is motivated by a problem from practice.

A model theory approach to structural limits

Jaroslav Nešetřil, Patrice Ossona de Mendez (2012)

Commentationes Mathematicae Universitatis Carolinae

The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.

A modification of the median of a tree

Bohdan Zelinka (1993)

Mathematica Bohemica

The concept of median of a tree is modified, considering only distances from the terminal vertices instead of distances from all vertices.

A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs

Sizhong Zhou, Fan Yang, Zhiren Sun (2016)

Discussiones Mathematicae Graph Theory

Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it is proved...

A new approach to chordal graphs

Ladislav Nebeský (2007)

Czechoslovak Mathematical Journal

By a chordal graph is meant a graph with no induced cycle of length ≥ 4 . By a ternary system is meant an ordered pair ( W , T ) , where W is a finite nonempty set, and T ⊆ W × W × W . Ternary systems satisfying certain axioms (A1)–(A5) are studied in this paper; note that these axioms can be formulated in a language of the first-order logic. For every finite nonempty set W , a bijective mapping from the set of all connected chordal graphs G with V ( G ) = W onto the set of all ternary systems ( W , T ) satisfying the axioms (A1)–(A5) is...

A New Characterization of Unichord-Free Graphs

Terry A. McKee (2015)

Discussiones Mathematicae Graph Theory

Unichord-free graphs are defined as having no cycle with a unique chord. They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to characterizing chordal graphs by minimal separators always inducing complete subgraphs). A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.

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