Results 181 to 190 of about 1,408,918 (247)

Explicit 3‐colorings for Exponential Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT In 1985, El‐Zahar and Sauer showed that the chromatic number of the direct product of two 4‐chromatic graphs is 4, establishing a nontrivial case of Hedetniemi's conjecture, which has since been refuted in general. Their proof uses the concept of an exponential graph, showing that if a graph H $H$ has no proper 3‐coloring, then the exponential
Adrien Argento, Pierre Charbit, Alantha Newman   +2 more
wiley   +1 more source

The Spectral Rrepresentation of a Discrete Version of Blackwell's Markov Chain. [PDF]

Entropy (Basel)
Nieznaj E.
europepmc   +1 more source

Flexible List Coloring of Graphs With Maximum Average Degree Less Than 3

Journal of Graph Theory, EarlyView.
ABSTRACT In the flexible list coloring problem, we consider a graph G $G$ and a color list assignment L $L$ on G $G$, as well as a subset U ⊆ V ( G ) $U\subseteq V(G)$ for which each u ∈ U $u\in U$ has a preferred color p ( u ) ∈ L ( u ) $p(u)\in L(u)$. Our goal is to find a proper L $L$‐coloring ϕ $\phi $ of G $G$ such that ϕ ( u ) = p ( u ) $\phi (u)=
Richard Bi, Peter Bradshaw
wiley   +1 more source

Genome rearrangements as double coset Markov chains. [PDF]

J Math Biol
Simper MA.
europepmc   +1 more source

Sparse Graphs With Local Covering Conditions on Edges

Journal of Graph Theory, EarlyView.
ABSTRACT In 1988, Erdős suggested the question of minimizing the number of edges in a connected n $n$‐vertex graph where every edge is contained in a triangle. Shortly after, Catlin, Grossman, Hobbs, and Lai resolved this in a stronger form. In this paper, we study a natural generalization of the question of Erdős in which we replace “triangle” with ...
Debsoumya Chakraborti, Amirali Madani, Anil Maheshwari, Babak Miraftab   +3 more
wiley   +1 more source

Exploring new lengths for q-ary quantum MDS codes with larger distance. [PDF]

PLoS One
He X, Wang J, Huang C, Chen Y.
europepmc   +1 more source

Path Degeneracy and Applications

Journal of Graph Theory, EarlyView.
ABSTRACT In this work, we relate girth and path‐degeneracy in classes with sub‐exponential expansion, with explicit bounds for classes with polynomial expansion and proper minor‐closed classes that are tight up to a constant factor (and tight up to second order terms if a classical conjecture on existence of g $g$‐cages is verified). As an application,
Yuquan Lin, Patrice Ossona de Mendez
wiley   +1 more source

Abelian varieties of prescribed order over finite fields. [PDF]

Math Ann
van Bommel R, Costa E, Li W, Poonen B, Smith A.   +4 more
europepmc   +1 more source

On Sparsity Conditions Guaranteeing a Fractional Coloring

Journal of Graph Theory, EarlyView.
ABSTRACT A graph has an ( a : b ) $(a:b)$ ‐coloring if there exists an assignment from the vertices to subsets of { 1 , … , a } $\{1,\ldots ,a\}$ with size b $b$ such that adjacent vertices are assigned disjoint subsets. Odd girth at least 2 k + 1 $2k+1$ is a necessary condition for a graph to have a ( 2 k + 1 : k ) $(2k+1:k)$‐coloring.
Ilkyoo Choi
wiley   +1 more source

Hadamard gate realization based on quantum Fourier transform for the creation of quantum numbers in the integrated optical domain. [PDF]

Sci Rep
Armaghani S, Rostami A.
europepmc   +1 more source