The total interval number of a graph

  title={The total interval number of a graph},
  author={Thomas Andreae and Martin Aigner},
  journal={J. Comb. Theory, Ser. B},
A representation f of a graph G is a mapping f which assigns to each vertex of G a non-empty collection of intervals on the real line so that two distinct vertices x and y are adjacent if and only if there are intervals I~f(x) and J~f(y) with InJ# a. We study the total interval number of G, defined as I(G) = minCL, VtGj If(x)l:fis a representation of G}. Let n be the number of vertices of G. Our main results on I(G) are: (a) If G is a tree then I(G)<L5n/4-3/4J for n > 3. (b) If G is a triangle… CONTINUE READING

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Publications referenced by this paper.
Showing 1-9 of 9 references

TROTTER AND F. HARARY, On double and multiple interval graphs

W T.
J. Graph Theory • 1978
View 3 Excerpts
Highly Influenced

WEST, Parameters of partial orders and graphs: Packing, covering, and representation, in “Graphs and Orders

D B.
(I. Rival, Ed.), • 1985

HARARY , On double and multiple interval graphs


A Note on Sub-Eulerian Graphs

Journal of Graph Theory • 1979
View 3 Excerpts

GRIGGS, Extremal values of the interval number of a graph, II, Discrete Math

J R.

MKJRTY, “Graph Theory with Applications,

View 1 Excerpt

Bounds on the number of disjoint spanning trees

J. Combin. Theory Set. B • 1974
View 2 Excerpts

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