Results 41 to 50 of about 80,953 (208)
On Kotzig's Perfect Set Problem of Hamiltonian Cycle Decompositions of the Complete Graph
Journal of Combinatorial Designs, EarlyView.ABSTRACT A Hamiltonian cycle decomposition (HCD) of K n ${K}_{n}$ is a set of Hamiltonian cycles in which each 1‐path of K n ${K}_{n}$ appears exactly once. A Dudeney set of K n ${K}_{n}$ is a set of Hamiltonian cycles in which each 2‐path of K n ${K}_{n}$ appears exactly once.
Nobuaki Mutoh
wiley +1 more source
Transforming Solutions for the Oberwolfach Problem into Solutions for the Spouse‐Loving Variant
Journal of Combinatorial Designs, EarlyView.ABSTRACT The Oberwolfach problem OP ( F ) $\mathrm{OP}(F)$, for a 2‐factor F $F$ of K n ${K}_{n}$, asks whether there exists a 2‐factorization of K n ${K}_{n}$ (if n $n$ is odd) or K n − I ${K}_{n}-I$ (if n $n$ is even) where each 2‐factor is isomorphic to F $F$. Here, I $I$ denotes any 1‐factor of K n ${K}_{n}$. For even n $n$, the problem OP( F ) $(F)
Maruša Lekše, Mateja Šajna
wiley +1 more source
Upper bounds of orders of automorphism groups of leafless metric graphs
AKCE International Journal of Graphs and CombinatoricsWe prove a tropical analogue of the theorem of Hurwitz: A leafless metric graph of genus [Formula: see text] has at most 12 automorphisms when g = 2 and [Formula: see text] automorphisms when [Formula: see text].
Yusuke Nakamura, JuAe Song
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R ( 5 , 5 ) ≤ 46 $R(5,5)\le 46$
Journal of Graph Theory, EarlyView.ABSTRACT We prove that the Ramsey number R ( 5 , 5 ) $R(5,5)$ is less than or equal to 46. The proof uses a combination of linear programming and checking a large number of cases by computer. All of the computational parts of the proof were independently implemented by both authors, with consistent results.
Vigleik Angeltveit, Brendan D. McKay
wiley +1 more source
Automorphism invariant measures and weakly generic automorphisms
Mathematical Logic Quarterly, 2022 AbstractLet be a countable ℵ0‐homogeneous structure. The primary motivation of this work is to study different amenability properties of (subgroups of) the automorphism group of ; the secondary motivation is to study the existence of weakly generic automorphisms of .
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Signed Projective Cubes, a Homomorphism Point of View
Journal of Graph Theory, EarlyView.ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen +2 more
wiley +1 more source
The automorphism group of Poisson algebras on k[x; y]
Қарағанды университетінің хабаршысы. Математика сериясы, 2017 Poisson algebras play a key role in the Hamiltonian mechanics, symplectic geometry and also are central in the study of quantum groups. At present, Poisson algebras are investigated by the many mathematicians of Russia, France, the USA, Brazil ...
U. Turusbekova, G. Azieva
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Bulletin of the Belgian Mathematical Society - Simon Stevin, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stroppel, Markus, van Maldeghem, Hendrik
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A Coarse Geometric Approach to Graph Layout Problems
Journal of Graph Theory, EarlyView.ABSTRACT We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are ...
Wanying Huang +3 more
wiley +1 more source
Distinguishing Cartesian Products of Countable Graphs
Discussiones Mathematicae Graph Theory, 2017 The distinguishing number D(G) of a graph G is the minimum number of colors needed to color the vertices of G such that the coloring is preserved only by the trivial automorphism.
Estaji Ehsan +4 more
doaj +1 more source