scholarly journals Optimal Distance Labeling for Interval Graphs and Related Graph Families

2008 ◽  
Vol 22 (3) ◽  
pp. 1239-1258 ◽  
Author(s):  
Cyril Gavoille ◽  
Christophe Paul
Keyword(s):  
Interval Graphs ◽  
Distance Labeling ◽  
Optimal Distance ◽  
Related Graph ◽  
Graph Families

scholarly journals Classes of graphs with restricted interval models

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Andrzej Proskurowski ◽  
Jan Arne Telle
Keyword(s):  
Maximum Clique ◽  
Interval Graphs ◽  
Induced Subgraph ◽  
Graph Theoretic ◽  
Graph Classes ◽  
International Audience ◽  
Forbidden Induced Subgraph ◽  
Nested Hierarchy ◽  
Graph Families

International audience We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs. We initiate a graph-theoretic study of subgraphs of q-proper interval graphs with maximum clique size k+1 and give an equivalent characterization of these graphs by restricted path-decomposition. By allowing the parameter q to vary from 0 to k, we obtain a nested hierarchy of graph families, from graphs of bandwidth at most k to graphs of pathwidth at most k. Allowing both parameters to vary, we have an infinite lattice of graph classes ordered by containment.

scholarly journals Removing Twins in Graphs to Break Symmetries

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1111
Author(s):  
Antonio González ◽  
María Luz Puertas
Keyword(s):  
Automorphism Groups ◽  
Upper Bounds ◽  
Unit Interval ◽  
Interval Graphs ◽  
Minimum Size ◽  
Lower And Upper Bounds ◽  
Graph Families ◽  
Arbitrary Graphs

Determining vertex subsets are known tools to provide information about automorphism groups of graphs and, consequently about symmetries of graphs. In this paper, we provide both lower and upper bounds of the minimum size of such vertex subsets, called the determining number of the graph. These bounds, which are performed for arbitrary graphs, allow us to compute the determining number in two different graph families such are cographs and unit interval graphs.

scholarly journals Classes of Graphs with $e$-Positive Chromatic Symmetric Function

10.37236/8211 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Angèle M. Foley ◽  
Chính T. Hoàng ◽  
Owen D. Merkel
Keyword(s):  
Symmetric Functions ◽  
Interval Graph ◽  
Unit Interval ◽  
Interval Graphs ◽  
Induced Subgraphs ◽  
Related Case ◽  
Graph Classes ◽  
Unit Interval Graph ◽  
Related Graph ◽  
Chromatic Symmetric Function

In the mid-1990s, Stanley and Stembridge conjectured that the chromatic symmetric functions of claw-free co-comparability (also called incomparability) graphs were $e$-positive. The quest for the proof of this conjecture has led to an examination of other, related graph classes. In 2013 Guay-Paquet proved that if unit interval graphs are $e$-positive, that implies claw-free incomparability graphs are as well. Inspired by this approach, we consider a related case and prove  that unit interval graphs whose complement is also a unit interval graph are $e$-positive.   We introduce the concept of strongly $e$-positive to denote a graph whose induced subgraphs are all $e$-positive, and conjecture that a graph is strongly $e$-positive if and only if it is (claw, net)-free.  

Fuzzy Labeling on Cycle Related Graph

2019 ◽  
Vol 7 (6) ◽  
pp. 1192-1194
Author(s):  
M.K. Pandurangan ◽  
T. Bharathi ◽  
S.Antony Vinoth
Keyword(s):  
Related Graph

scholarly journals Claw-free graphs. III. Circular interval graphs

2008 ◽  
Vol 98 (4) ◽  
pp. 812-834 ◽  
Author(s):  
Maria Chudnovsky ◽  
Paul Seymour
Keyword(s):  
Interval Graphs

scholarly journals Computing the branchwidth of interval graphs

2005 ◽  
Vol 145 (2) ◽  
pp. 266-275 ◽  
Author(s):  
Ton Kloks ◽  
Jan Kratochvíl ◽  
Haiko Müller
Keyword(s):  
Interval Graphs
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