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- W35570633 abstract "A classical result due to Steinitz states that a graph is isomorphic to the graph of some 3-dimensional polytope P if and only if it is planar and 3-connected. If a graph G is isomorphic to the graph of a 3-dimensional polytope inscribed in a sphere, it is said to be of inscribable type. The problem of determining which graphs are of inscribable type dates back to 1832 and was open until Rivin proved a characterization in terms of the existence of a strictly feasible solution to a system of linear equations and inequalities which we call sys(G), which, surprisingly, also appears in the context of the Traveling Salesman Problem. Using such a characterization, various classes of graphs of inscribable type can be described. Dillencourt and Smith gave a characterization of 3-connected 3-regular planar graphs that are of inscribable and a linear-time algorithm for recognizing such graphs. In this paper, their results are generalized to r-edge-connected r-regular graphs for odd r ≥ 3 in the context of the existence of strictly feasible solutions to sys(G). An answer to an open question raised by D. Eppstein concerning the inscribability of 4-regular graphs is also given." @default.
- W35570633 created "2016-06-24" @default.
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- W35570633 date "2013-10-01" @default.
- W35570633 modified "2023-09-23" @default.
- W35570633 title "On r-Edge-Connected r-Regular Bricks and Braces and Inscribability" @default.
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- W35570633 doi "https://doi.org/10.13189/ms.2013.010305" @default.
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