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West, Douglas B. Kratzke, Thomas Martin 2014-12-16T06:18:21Z 2014-12-16T06:18:21Z 10000-01-01 1988 1988 An interval representation (or simply representation) R of a graph G is a collection of finite sets $\{R(\nu):\nu \in V(G)\}$ of closed bounded intervals so that $u \leftrightarrow \nu$ if and only if there exist $\theta\sb{u} \in R(u), \theta\sb{\nu} \in R(\nu)$ with $\theta\sb{u} \cap \theta\sb{\nu} \not= \emptyset$. The size of a representation is the number of intervals in the entire collection. The total interval number of G is the size of the smallest representation of G and is denoted I(G). This thesis studies I by proving best possible upper bounds for several classes of graphs. For some classes, the bounds are in terms of n, the number of vertices and for some classes, the bounds are in terms of m, the number of edges. The main result is that for planar graphs, $I(G) \leq 2n(G) - 3$. Made available in DSpace on 2014-12-16T06:18:21Z (GMT). No. of bitstreams: 1 8815372.pdf: 5483196 bytes, checksum: 87e060f0b586a5ddab657ced37f050da (MD5) Previous issue date: 1988 Embargo set by: Seth Robbins for item 71430 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 123 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988. http://hdl.handle.net/2142/71264 (UMI)AAI8815372 Mathematics Computer Science The Total Interval Number of a Graph text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.