Results 61 to 70 of about 789,258 (121)
Partitioning the projective plane into two incidence‐rich parts
Journal of Combinatorial Designs, Volume 32, Issue 12, Page 703-714, December 2024.Abstract An internal or friendly partition of a vertex set V ( G ) $V(G)$ of a graph G $G$ is a partition to two nonempty sets A ∪ B $A\cup B$ such that every vertex has at least as many neighbours in its own class as in the other one. Motivated by Diwan's existence proof on internal partitions of graphs with high girth, we give constructive proofs for
Zoltán Lóránt Nagy
wiley +1 more source
3 List Coloring Graphs of Girth at least Five on Surfaces [PDF]
arXiv, 2017 Grotzsch proved that every triangle-free planar graph is 3-colorable. Thomassen proved that every planar graph of girth at least five is 3-choosable. As for other surfaces, Thomassen proved that there are only finitely many 4-critical graphs of girth at least five embeddable in any fixed surface.
arxiv
Near-colorings: non-colorable graphs and NP-completeness [PDF]
, 2013 A graph G is (d_1,..,d_l)-colorable if the vertex set of G can be partitioned into subsets V_1,..,V_l such that the graph G[V_i] induced by the vertices of V_i has maximum degree at most d_i for all 1
Montassier, Mickael, Ochem, Pascal
core
Girth, words and diameter [PDF]
arXiv, 2019 We study the girth of Cayley graphs of finite classical groups G on random sets of generators. Our main tool is an essentially best possible bound we obtain on the probability that a given word w takes the value 1 when evaluated in G in terms of the length of w, which has additional applications. We also study the girth of random directed Cayley graphs
arxiv
Secret sharing on large girth graphs [PDF]
arXiv, 2017 We investigate graph based secret sharing schemes and its information ratio, also called complexity, measuring the maximal amount of information the vertices has to store. It was conjectured that in large girth graphs, where the interaction between far away nodes is restricted to a single path, this ratio is bounded.
arxiv
High-girth near-Ramanujan graphs with lossy vertex expansion [PDF]
arXiv, 2020 Kahale proved that linear sized sets in $d$-regular Ramanujan graphs have vertex expansion $\sim\frac{d}{2}$ and complemented this with construction of near-Ramanujan graphs with vertex expansion no better than $\frac{d}{2}$. However, the construction of Kahale encounters highly local obstructions to better vertex expansion.
arxiv
Design of Low-Density Parity-Check Code Pair for Joint Source-Channel Coding Systems Based on Graph Theory. [PDF]
Entropy (Basel), 2023 Lv Y, He J, Xu W, Wang L.
europepmc +1 more source
Analytical lower bounds for the size of elementary trapping sets of variable-regular LDPC codes with any girth and irregular ones with girth 8 [PDF]
arXiv, 2017 In this paper we give lower bounds on the size of $(a,b)$ elementary trapping sets (ETSs) belonging to variable-regular LDPC codes with any girth, $g$, and irregular ones with girth 8, where $a$ is the size, $b$ is the number of degree-one check nodes and satisfy the inequality $\frac{b}{a}<1$.
arxiv
Quantum LDPC Codes Based on Cocyclic Block Matrices. [PDF]
Entropy (Basel), 2023 Li Y, Guo Y.
europepmc +1 more source
The Coloring Game on Planar Graphs with Large Girth, by a result on Sparse Cactuses [PDF]
arXiv, 2015 We denote by $\chi$ g (G) the game chromatic number of a graph G, which is the smallest number of colors Alice needs to win the coloring game on G. We know from Montassier et al. [M. Montassier, P. Ossona de Mendez, A. Raspaud and X. Zhu, Decomposing a graph into forests, J. Graph Theory Ser.
arxiv