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- W2916909455 abstract "The aim of this note is to advance the refining of the Erdős-Kelly result on graphical inducing regularization. The operation of inducing regulation (on graphs or multigraphs) with prescribed maximum vertex degree is originated by D. König in 1916. As is shown by Chartrand and Lesniak in their textbook Graphs & Digraphs (1996), an iterated construction for graphs can result in a regularization with many new vertices. Erdős and Kelly have presented (1963, 1967) a simple and elegant numerical method of determining for any simple (n)-vertex graph (G) with maximum vertex degree (Delta), the exact minimum number, say (theta =theta(G)), of new vertices in a (Delta)-regular graph (H) which includes (G) as an induced subgraph. The number (theta(G)), which we call the cost of regulation of (G), has been upper-bounded by the order of (G), the bound being attained for each (nge4), e.g. then the edge-deleted complete graph (K_n-e) has (theta=n). For (nge 4), we present all factors of (K_n) with (theta=n) and next (theta=n-1). Therein in case (theta=n-1) and (n) odd only, we show that a specific extra structure, non-matching, is required." @default.
- W2916909455 created "2019-03-02" @default.
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- W2916909455 date "2019-01-01" @default.
- W2916909455 modified "2023-10-16" @default.
- W2916909455 title "A partial refining of the Erdős-Kelly regulation" @default.
- W2916909455 doi "https://doi.org/10.7494/opmath.2019.39.3.355" @default.
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