Results 81 to 90 of about 143,400 (232)
The IC-Indices of Complete Bipartite Graphs [PDF]
The Electronic Journal of Combinatorics, 2008 Let $G$ be a connected graph, and let $f$ be a function mapping $V(G)$ into ${\Bbb N}$. We define $f(H)=\sum_{v\in{V(H)}}f(v)$ for each subgraph $H$ of $G$. The function $f$ is called an IC-coloring of $G$ if for each integer $k$ in the set $\{1,2,\cdots,f(G)\}$ there exists an (induced) connected subgraph $H$ of $G$ such that $f(H)=k$, and the IC ...
Shiue, Chin-Lin, Fu, Hung-Lin
openaire +2 more sources
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
wiley +1 more source
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
Reconfiguring k-colourings of Complete Bipartite Graphs
, 2016 Let H be a graph, and k ≥ χ(H) an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices ...
Marcel Celaya +3 more
semanticscholar +1 more source
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
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
Bipartite 2‐Factorizations of Complete Multipartite Graphs [PDF]
Journal of Graph Theory, 2014 AbstractIt is shown that if K is any regular complete multipartite graph of even degree, and F is any bipartite 2‐factor of K, then there exists a factorization of K into F; except that there is no factorization of K6, 6 into F when F is the union of two disjoint 6‐cycles.
Bryant, Darryn +2 more
openaire +3 more sources
Orientations of Graphs With at Most One Directed Path Between Every Pair of Vertices
Journal of Graph Theory, EarlyView.ABSTRACT Given a graph G $G$, we say that an orientation D $D$ of G $G$ is a KT orientation if, for all u , v ∈ V ( D ) $u,v\in V(D)$, there is at most one directed path (in any direction) between u $u$ and v $v$. Graphs that admit such orientations have been used to construct graphs with large chromatic number and small clique number that served as ...
Barbora Dohnalová +3 more
wiley +1 more source