scholarly journals A 2()n algorithm for k-cycle in minor-closed graph families

2020 ◽  
Vol 842 ◽  
pp. 74-85
Author(s):  
Raphael Yuster
Keyword(s):  
Closed Graph ◽  
Graph Families

scholarly journals Densities of Minor-Closed Graph Families

10.37236/408 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
David Eppstein
Keyword(s):  
Order Type ◽  
Closed Graph ◽  
Simple Graphs ◽  
Minimal Graphs ◽  
Vertex Graph ◽  
Graph Families ◽  
A Minor ◽  
Cluster Points

We define the limiting density of a minor-closed family of simple graphs $\mathcal{F}$ to be the smallest number $k$ such that every $n$-vertex graph in $\mathcal{F}$ has at most $kn(1+o(1))$ edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, well-ordered, and closed; its order type is at least $\omega^\omega$. It is the closure of the set of densities of density-minimal graphs, graphs for which no minor has a greater ratio of edges to vertices. By analyzing density-minimal graphs of low densities, we find all limiting densities up to the first two cluster points of the set of limiting densities, $1$ and $3/2$. For multigraphs, the only possible limiting densities are the integers and the superparticular ratios $i/(i+1)$.

scholarly journals Density of Chromatic Roots in Minor-Closed Graph Families

2018 ◽  
Vol 27 (6) ◽  
pp. 988-998 ◽  
Author(s):  
THOMAS J. PERRETT ◽  
CARSTEN THOMASSEN
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Classical Result ◽  
Golden Ratio ◽  
Chromatic Polynomial ◽  
Closed Graph ◽  
Small Interval ◽  
Chromatic Polynomials ◽  
Graph Families ◽  
Chromatic Roots

We prove that the roots of the chromatic polynomials of planar graphs are dense in the interval between 32/27 and 4, except possibly in a small interval around τ + 2 where τ is the golden ratio. This interval arises due to a classical result of Tutte, which states that the chromatic polynomial of every planar graph takes a positive value at τ + 2. Our results lead us to conjecture that τ + 2 is the only such number less than 4.

Diameter and Treewidth in Minor-Closed Graph Families, Revisited

Algorithmica ◽  
2004 ◽  
Vol 40 (3) ◽  
pp. 211-215 ◽  
Author(s):  
Erik D. Demaine ◽  
Mohammad Taghi Hajiaghayi
Keyword(s):  
Closed Graph ◽  
Graph Families

scholarly journals Diameter and Treewidth in Minor-Closed Graph Families

Algorithmica ◽  
2000 ◽  
Vol 27 (3) ◽  
pp. 275-291 ◽  
Author(s):  
D. Eppstein
Keyword(s):  
Closed Graph ◽  
Graph Families

scholarly journals R-continuous functions

1992 ◽  
Vol 15 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Ch. Konstadilaki-Savvapoulou ◽  
D. Janković
Keyword(s):  
Continuous Functions ◽  
Strong Form ◽  
Topological Spaces ◽  
Strong Continuity ◽  
Closed Graph ◽  
Continuity Properties

A strong form of continuity of functions between topological spaces is introduced and studied. It is shown that in many known results, especially closed graph theorems, functions under consideration areR-continuous. Several results in the literature concerning strong continuity properties are generalized and/or improved.

scholarly journals Strictly barrelled disks in inductive limits of quasi-(LB)-spaces

1996 ◽  
Vol 19 (4) ◽  
pp. 727-732
Author(s):  
Carlos Bosch ◽  
Thomas E. Gilsdorf
Keyword(s):  
Convex Space ◽  
Inductive Limit ◽  
Linear Span ◽  
Locally Convex Space ◽  
Minkowski Functional ◽  
Closed Graph ◽  
Inductive Limits ◽  
Locally Convex ◽  
Barrelled Space

A strictly barrelled diskBin a Hausdorff locally convex spaceEis a disk such that the linear span ofBwith the topology of the Minkowski functional ofBis a strictly barrelled space. Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi-(LB)-space is bounded. It is shown that a locally strictly barrelled quasi-(LB)-space is locally complete. Also, we show that a regular inductive limit of quasi-(LB)-spaces is locally complete if and only if each closed bounded disk is a strictly barrelled disk in one of the constituents.

scholarly journals The simultaneous metric dimension of graph families

2016 ◽  
Vol 198 ◽  
pp. 241-250 ◽  
Author(s):  
Yunior Ramírez-Cruz ◽  
Ortrud R. Oellermann ◽  
Juan A. Rodríguez-Velázquez
Keyword(s):  
Metric Dimension ◽  
Graph Families ◽  
Simultaneous Metric Dimension

B(?)-spaces and the closed graph theorem

1964 ◽  
Vol 153 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Taqdir Husain
Keyword(s):  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem
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