Results 91 to 100 of about 153,964 (249)
Long Induced Paths in K s , s ${K}_{s,s}$‐Free Graphs
Journal of Graph Theory, EarlyView.ABSTRACT More than 40 years ago, Galvin, Rival, and Sands showed that every K s , s ${K}_{s,s}$‐free graph containing an n $n$‐vertex path must contain an induced path of length f ( n ) $f(n)$, where f ( n ) → ∞ $f(n)\to \infty $ as n → ∞ $n\to \infty $. Recently, it was shown by Duron, Esperet, and Raymond that one can take f ( n ) = ( log log n ) 1 /
Zach Hunter +3 more
wiley +1 more source
Edge‐Length Preserving Embeddings of Graphs Between Normed Spaces
Journal of Graph Theory, EarlyView.ABSTRACT The concept of graph embeddability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces into a given normed space. A finite simple graph G = ( V , E ) $G=(V,E)$ is said to be ( X , Y ) $(X,Y)$‐embeddable if any set of induced edge lengths from an ...
Sean Dewar +3 more
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Complexity of Hamiltonian Cycle Reconfiguration
Algorithms, 2018 The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained ...
Asahi Takaoka
doaj +1 more source
Groups having complete bipartite divisor graphs for their conjugacy class sizes [PDF]
, 2013 Given a finite group G, the bipartite divisor graph for its conjugacy class sizes is the bipartite graph with bipartition consisting of the set of conjugacy class sizes of G-Z (where Z denotes the centre of G) and the set of prime numbers that divide ...
Hafezieh, Roghayeh, Spiga, Pablo
core
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
Extremal Betti numbers of some classes of binomial edge ideals [PDF]
, 2013 Let $G$ be a cycle or a complete bipartite graph. We show that the binomial edge ideal $J_{G}$ and its initial ideal with respect to the lexicographic order have the same extremal Betti ...
Dokuyucu, Ahmet
core
Fractional Balanced Chromatic Number and Arboricity of Planar (Signed) Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A balanced ( p , q ) $(p,q)$‐coloring of a signed graph ( G , σ ) $(G,\sigma )$ is an assignment of q $q$ colors to each vertex of G $G$ from a platter of p $p$ colors, such that each color class induces a balanced set (a set that does not induce a negative cycle).
Reza Naserasr +3 more
wiley +1 more source
Fractional List Packing for Layered Graphs
Journal of Graph Theory, EarlyView.ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
wiley +1 more source
Packing trees in complete bipartite graphs
Discussiones Mathematicae Graph Theory, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley +1 more source