Matches in SemOpenAlex for { <https://semopenalex.org/work/W2896422451> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W2896422451 abstract "The concept of a $1$-rotational factorization of a complete graph under a finite group $G$ was studied in detail by Buratti and Rinaldi. They found that if $G$ admits a $1$-rotational $2$-factorization, then the involutions of $G$ are pairwise conjugate. We extend their result by showing that if a finite group $G$ admits a $1$-rotational $k=2^nm$-factorization where $ngeq 1$, and $m$ is odd, then $G$ has at most $m(2^n-1)$ conjugacy classes containing involutions. Also, we show that if $G$ has exactly $m(2^n-1)$ conjugacy classes containing involutions, then the product of a central involution with an involution in one conjugacy class yields an involution in a different conjugacy class. We then demonstrate a method of constructing a $1$-rotational $2n$-factorization under $G times mathbb{Z}_n$ given a $1$-rotational $2$-factorization under a finite group $G$. This construction, given a $1$-rotational solution to the Oberwolfach problem $OP(a_{infty},a_1, a_2 cdots, a_n)$, allows us to find a solution to $OP(2a_{infty}-1,^2a_1, ^2a_2cdots, ^2a_n)$ when the $a_i$'s are even ($i neq infty$), and $OP(p(a_{infty}-1)+1, ^pa_1, ^pa_2 cdots, ^pa_n)$ when $p$ is an odd prime, with no restrictions on the $a_i$'s." @default.
- W2896422451 created "2018-10-26" @default.
- W2896422451 creator A5022955004 @default.
- W2896422451 creator A5023876779 @default.
- W2896422451 date "2018-10-23" @default.
- W2896422451 modified "2023-09-27" @default.
- W2896422451 title "A Method to Construct $1$-Rotational Factorizations of Complete Graphs and Solutions to the Oberwolfach Problem" @default.
- W2896422451 cites W1546790517 @default.
- W2896422451 cites W1605023168 @default.
- W2896422451 cites W1662464937 @default.
- W2896422451 cites W1861483862 @default.
- W2896422451 cites W1945346921 @default.
- W2896422451 cites W1966442544 @default.
- W2896422451 cites W1977067446 @default.
- W2896422451 cites W1979984579 @default.
- W2896422451 cites W2002197583 @default.
- W2896422451 cites W2003308875 @default.
- W2896422451 cites W2045234274 @default.
- W2896422451 cites W2048156596 @default.
- W2896422451 cites W2160398802 @default.
- W2896422451 hasPublicationYear "2018" @default.
- W2896422451 type Work @default.
- W2896422451 sameAs 2896422451 @default.
- W2896422451 citedByCount "0" @default.
- W2896422451 crossrefType "posted-content" @default.
- W2896422451 hasAuthorship W2896422451A5022955004 @default.
- W2896422451 hasAuthorship W2896422451A5023876779 @default.
- W2896422451 hasConcept C11413529 @default.
- W2896422451 hasConcept C114614502 @default.
- W2896422451 hasConcept C121332964 @default.
- W2896422451 hasConcept C132525143 @default.
- W2896422451 hasConcept C187834632 @default.
- W2896422451 hasConcept C2777404646 @default.
- W2896422451 hasConcept C2781311116 @default.
- W2896422451 hasConcept C33923547 @default.
- W2896422451 hasConcept C62520636 @default.
- W2896422451 hasConcept C87945829 @default.
- W2896422451 hasConceptScore W2896422451C11413529 @default.
- W2896422451 hasConceptScore W2896422451C114614502 @default.
- W2896422451 hasConceptScore W2896422451C121332964 @default.
- W2896422451 hasConceptScore W2896422451C132525143 @default.
- W2896422451 hasConceptScore W2896422451C187834632 @default.
- W2896422451 hasConceptScore W2896422451C2777404646 @default.
- W2896422451 hasConceptScore W2896422451C2781311116 @default.
- W2896422451 hasConceptScore W2896422451C33923547 @default.
- W2896422451 hasConceptScore W2896422451C62520636 @default.
- W2896422451 hasConceptScore W2896422451C87945829 @default.
- W2896422451 hasLocation W28964224511 @default.
- W2896422451 hasOpenAccess W2896422451 @default.
- W2896422451 hasPrimaryLocation W28964224511 @default.
- W2896422451 hasRelatedWork W1884855618 @default.
- W2896422451 hasRelatedWork W1975923819 @default.
- W2896422451 hasRelatedWork W1986977567 @default.
- W2896422451 hasRelatedWork W2007969418 @default.
- W2896422451 hasRelatedWork W2032265058 @default.
- W2896422451 hasRelatedWork W2073527169 @default.
- W2896422451 hasRelatedWork W2098979446 @default.
- W2896422451 hasRelatedWork W2580290891 @default.
- W2896422451 hasRelatedWork W2595582299 @default.
- W2896422451 hasRelatedWork W2762248185 @default.
- W2896422451 hasRelatedWork W2772298734 @default.
- W2896422451 hasRelatedWork W2797148876 @default.
- W2896422451 hasRelatedWork W2892616364 @default.
- W2896422451 hasRelatedWork W2949511201 @default.
- W2896422451 hasRelatedWork W2949667504 @default.
- W2896422451 hasRelatedWork W2964269067 @default.
- W2896422451 hasRelatedWork W2965390360 @default.
- W2896422451 hasRelatedWork W2981608402 @default.
- W2896422451 hasRelatedWork W2998818043 @default.
- W2896422451 hasRelatedWork W2522114319 @default.
- W2896422451 isParatext "false" @default.
- W2896422451 isRetracted "false" @default.
- W2896422451 magId "2896422451" @default.
- W2896422451 workType "article" @default.