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
A multidimensional, efficient, and secure data query based on privacy preservation in vehicular ad hoc networks. [PDF]
PLoS OneZhao X, Dong G.
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
The Phylogenetic Structure of β -diversity: Covariance Matrix Sparsification of Critical Beta-splitting Trees. [PDF]
Bull Math BiolSvihla SP, Lladser ME.
europepmc +1 more source
Saturated Partial Embeddings of Planar Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In this work, we study how far one can deviate from optimal behavior when embedding a planar graph. For a planar graph G $G$, we say that a plane subgraph H ⊆ G $H\subseteq G$ is a plane‐saturated subgraph if adding any edge (possibly with new vertices) to H $H$ would either violate planarity or make the resulting graph no longer a subgraph of
Alexander Clifton, Nika Salia
wiley +1 more source
Genome rearrangements as double coset Markov chains. [PDF]
J Math BiolSimper MA.
europepmc +1 more source
Equivalent Formulation of Thomassen's Conjecture Using Tutte Paths in Claw‐Free Graphs
Journal of Graph Theory, EarlyView.ABSTRACT We continue studying Thomassen's conjecture (every 4‐connected line graph has a Hamilton cycle) in the direction of a recently shown equivalence with Jackson's conjecture (every 2‐connected claw‐free graph has a Tutte cycle), and we extend the equivalent formulation as follows: In every connected claw‐free graph, any two vertices are connected
Adam Kabela +2 more
wiley +1 more source
On Algebraic Properties of Primitive Eisenstein Integers with Applications in Coding Theory. [PDF]
Entropy (Basel)Hadi A +3 more
europepmc +1 more source
Obstructions for Homomorphisms to Odd Cycles in Series‐Parallel Graphs
Journal of Graph Theory, EarlyView.ABSTRACT For a graph H $H$, an H $H$‐colouring of a graph G $G$ is a vertex mapping ϕ : V ( G ) → V ( H ) $\phi :V(G)\to V(H)$ such that adjacent vertices are mapped to adjacent vertices. A graph G $G$ is C 2 k + 1 ${C}_{2k+1}$‐critical if G $G$ has no C 2 k + 1 ${C}_{2k+1}$‐colouring but every proper subgraph of G $G$ has a C 2 k + 1 ${C}_{2k+1 ...
Eun‐Kyung Cho +3 more
wiley +1 more source
A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with <i>p</i>-Modular Lattice Constructions. [PDF]
Entropy (Basel)Khodaiemehr H +5 more
europepmc +1 more source