Zobrazeno 1 - 10
of 21
pro vyhledávání: '"05C51, 05C70"'
Publikováno v:
J. Combin. Des 27 (2019), 251-260
We prove that $K_n+I$, the complete graph of an even order with a $1$-factor duplicated, admits a decomposition into $2$-factors, each a disjoint union of cycles of length $m \geq 5$ if and only if $m \mid n$, except possibly when $m$ is odd and $n=4
Externí odkaz:
http://arxiv.org/abs/2407.21745
The generalized Oberwolfach problem asks for a decomposition of a graph $G$ into specified 2-regular spanning subgraphs $F_1,\ldots, F_k$, called factors. The classic Oberwolfach problem corresponds to the case when all of the factors are pairwise is
Externí odkaz:
http://arxiv.org/abs/2308.04307
Autor:
Traetta, Tommaso
For every $2$-regular graph $F$ of order $v$, the Oberwolfach problem $OP(F)$ asks whether there is a $2$-factorization of $K_v$ ($v$ odd) or $K_v$ minus a $1$-factor ($v$ even) into copies of $F$. Posed by Ringel in 1967 and extensively studied ever
Externí odkaz:
http://arxiv.org/abs/2306.12713
In this paper, factorizations of the complete symmetric digraph $K_v^*$ into uniform factors consisting of directed even cycle factors are studied as a generalization of the undirected Hamilton-Waterloo Problem. It is shown, with a few possible excep
Externí odkaz:
http://arxiv.org/abs/2306.12209
Autor:
Francetić, Nevena, Šajna, Mateja
We examine the necessary and sufficient conditions for a complete symmetric equipartite digraph $K_{n[m]}^\ast$ with $n$ parts of size $m$ to admit a resolvable decomposition into directed cycles of length $t$. We show that the obvious necessary cond
Externí odkaz:
http://arxiv.org/abs/2303.04308
The Directed Hamilton-Waterloo Problem asks for a directed $2$-factorization of the complete symmetric digraph $K_v^*$ where there are two non-isomorphic $2$-factors. In the uniform version of the problem, factors consist of either directed $m$-cycle
Externí odkaz:
http://arxiv.org/abs/2209.14588
We investigate the maximum size of graph families on a common vertex set of cardinality $n$ such that the symmetric difference of the edge sets of any two members of the family satisfies some prescribed condition. We solve the problem completely for
Externí odkaz:
http://arxiv.org/abs/2202.06810
Autor:
Stawiski, Marcin
Let $\mathcal{H}=\{H_i: i<\alpha \}$ be an indexed family of graphs for some ordinal number $\alpha$. $\mathcal{H}$-decomposition of a graph $G$ is a family $\mathcal{G}=\{G_i: i<\alpha \}$ of edge-disjoint subgraphs of $G$ such that $G_i$ is isomorp
Externí odkaz:
http://arxiv.org/abs/2103.07913
Autor:
Botler, Fábio, Hoffmann, Luiz
A $P_\ell$-decomposition of a graph $G$ is a set of paths with $\ell$ edges in $G$ that cover the edge set of $G$. Favaron, Genest, and Kouider (2010) conjectured that every $(2k+1)$-regular graph that contains a perfect matching admits a $P_{2k+1}$-
Externí odkaz:
http://arxiv.org/abs/2012.05145
In contrast with Kotzig's result that the line graph of a $3$-regular graph $X$ is Hamilton decomposable if and only if $X$ is Hamiltonian, we show that for each integer $k\geq 4$ there exists a simple non-Hamiltonian $k$-regular graph whose line gra
Externí odkaz:
http://arxiv.org/abs/1710.06037