article · SIAM Journal on Algebraic and Discrete Methods · 1982
The Interval Count of a Graph
Rochelle Leibowitz, Susan F. Assmann, G. W. Peck
Cited by 14Abstract and details only
Abstract
The interval count of an interval graph G is the minimum number of different interval sizes needed to represent the vertices of G, where two vertices are adjacent if and only if their intervals intersect. We show that if G is an interval graph and for some vertex x, $G - \{ x \}$ has interval count one, then G has interval count two or less. We also show how to construct examples of interval graphs where the interval count of G exceeds that of $G - \{ x \}$ by at least two when the latter number is two or more.
Cite this paper
Leibowitz, R., Assmann, S. F., & Peck, G. W. (1982). The Interval Count of a Graph. SIAM Journal on Algebraic and Discrete Methods, 3(4), 485–494. https://doi.org/10.1137/0603049
Leibowitz, Rochelle, et al. “The Interval Count of a Graph.” SIAM Journal on Algebraic and Discrete Methods, vol. 3, no. 4, 1982, pp. 485–94, https://doi.org/10.1137/0603049.
Leibowitz, Rochelle, Susan F. Assmann, and G. W. Peck. 1982. “The Interval Count of a Graph.” SIAM Journal on Algebraic and Discrete Methods 3 (4): 485–94. https://doi.org/10.1137/0603049.
Leibowitz, R., Assmann, S.F. and Peck, G.W. (1982) ‘The Interval Count of a Graph’, SIAM Journal on Algebraic and Discrete Methods, 3(4), pp. 485–494. Available at: https://doi.org/10.1137/0603049.
@article{leibowitz1982interval,
title = {{The Interval Count of a Graph}},
author = {Leibowitz, Rochelle and Assmann, Susan F. and Peck, G. W.},
journal = {SIAM Journal on Algebraic and Discrete Methods},
volume = {3},
number = {4},
pages = {485--494},
year = {1982},
doi = {10.1137/0603049}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.