On the maximum genus of a graph
Web1 de jun. de 1999 · A lower bound on the maximum genus of a 3-regular graph involving girth is provided. The lower bound is tight, it improves a bound of Huang and Liu. In this … Web12 de abr. de 2024 · Observational studies revealed altered gut microbial composition in patients with allergic diseases, which illustrated a strong association between the gut …
On the maximum genus of a graph
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Web1 de dez. de 2011 · We define the maximum genus, γM(G), of a connected graph G to be the largest genus γ(N) for compact orientable 2-manifolds N in which G has a 2-cell …
Webdetermining the minimum genus of a graph is NP-complete. There are some xed classes of graphs for which the minimum and maximum genus is known, but there will usually be many embeddings with a genus between these two values. Therefore, given a graph G, and a positive integer g, one could ask for the number of embeddings of Gof genus g. Web1 de jul. de 2024 · Let Z ( G) denote the cardinality of a maximum NSIS of G. A nonseparating independent set containing Z ( G) vertices is called the maximum …
Web1 de mar. de 1994 · We present a formula for the maximum (orientable) genus of the surface on which a graph has a relative embedding with respect to a set of closed … Web1 de dez. de 2011 · Lower bounds on the maximum genus are obtained by bounding from below the size of these odd subgraphs. As a special case, upper-embeddability of a class of graphs is caused by an absence of such subgraphs. A well-known theorem stating that every 4-edge-connected graph is upper-embeddable is a straightforward corollary of the …
WebThe maximum genus 7M(G) of a connected graph G is defined to be the maximum integer k such that there exists a cellular imbedding of G into the orientable surface of genus k. From the Euler polyhedral equation, we see that the maximum genus of a graph has the obvious upper bound "~'M(G) ~ L,B(G)/2J,
Web15 de set. de 2016 · According to this three approaches, we can construct exponentially many minimum genus embeddings of complete graph K 12s+8 in orientable surfaces, which show that there are at least \frac {10} {3} \times (\frac {200} {9})^s distinct minimum genus embeddings for K 12s+8 in orientable surfaces. current 10 year ust yieldsWebIt is proved that the number 1 is a limit point of the set of possible values for average genus and that the complete graph K4 is the only 3-connected graph whose average genus is … current 10 year t bill rates usaWeb27 de dez. de 2024 · In this case, the graph shows the function {eq}y\ =\ 12sin(x)\ -\ 0.1x^2 {/eq}. The red point identifies a local maximum on the graph. At that point, the graph … current 15 year fha refinance ratesWeb1 de jun. de 1972 · The maximum genus of G, denoted by γM ( G ), is the largest integer k such that G can be 2-cell imbedded in Sk. This paper characterizes those graphs G for which γ ( G) = γM ( G ). As part of this characterization, it is shown that γM ( G) = 0 if and only if G does not contain a subgraph isomorphic to a subdivision of one of two given … current 15 year mortgage rateWeb24 de mar. de 2024 · The genus of a graph is the minimum number of handles that must be added to the plane to embed the graph without any crossings. A graph with genus 0 is … current 15 year lending rateWebIn this paper we determine the maximum genus of a graph by using the matching number of the intersection graph of a basis of its cycle space. Our result is a common … current 15 year interest rate mortgageWebAbstractNot all rational numbers are possibilities for the average genus of an individual graph. The smallest such numbers are determined, and varied examples are constructed to demonstrate ... How to determine the maximum genus of a graph J. Comb. Theory Ser.B 1979 26 217 225 0403.05035 10.1016/0095-8956(79)90058-3 532590 Google Scholar … current 118th congress