Results 111 to 120 of about 1,680,672 (163)
Towards Characterization of Five‐List‐Colorability of Toroidal Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Through computer‐assisted enumeration, we list minimal obstructions for 5‐choosability of graphs on the torus with the following additional property: There exists a cyclic system of non‐contractible triangles around the torus where the consecutive triangles are at distance at most four.
Zdeněk Dvořák +1 more
wiley +1 more source
On Strongly and Robustly Critical Graphs
Journal of Graph Theory, EarlyView.ABSTRACT In extremal combinatorics, it is common to focus on structures that are minimal with respect to a certain property. In particular, critical and list‐critical graphs occupy a prominent place in graph coloring theory. Stiebitz, Tuza, and Voigt introduced strongly critical graphs, i.e., graphs that are k $k$‐critical yet L $L$‐colorable with ...
Anton Bernshteyn +3 more
wiley +1 more source
Sensitivity and Hamming Graphs
Journal of Graph Theory, EarlyView.ABSTRACT For any m ≥ 3 $m\ge 3$ we show that the Hamming graph H ( n , m ) $H(n,m)$ admits an imbalanced partition into m $m$ sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong m $m$‐ary Sensitivity Conjecture of Asensio, García‐Marco, and Knauer.
Sara Asensio +3 more
wiley +1 more source
Tight Bounds for Hypercube Minor‐Universality
Journal of Graph Theory, EarlyView.ABSTRACT A graph G $G$ is m $m$‐minor‐universal if every graph H $H$ with at most m $m$ edges and no isolated vertices is contained as a minor in G $G$. Recently, Benjamini, Kalifa and Tzalik proved that there is an absolute constant c>0 $c\gt 0$ such that the d $d$‐dimensional hypercube Qd ${Q}_{d}$ is (c⋅2d/d $c\cdot {2}^{d}/d$)‐minor‐universal ...
Emma Hogan +5 more
wiley +1 more source
An Improved Quasi‐Isometry Between Graphs of Bounded Cliquewidth and Graphs of Bounded Treewidth
Journal of Graph Theory, EarlyView.ABSTRACT Cliquewidth is a dense analogue of treewidth. It can be deduced from recent results by Hickingbotham [arXiv:2501.10840] and Nguyen, Scott, and Seymour [arXiv:2501.09839] that graphs of bounded cliquewidth are quasi‐isometric to graphs of bounded treewidth.
Marc Distel
wiley +1 more source
Upper Bounds on the Minimum Size of Feedback Arc Set of Directed Multigraphs With Bounded Degree
Journal of Graph Theory, EarlyView.ABSTRACT An oriented multigraph is a directed multigraph without directed 2‐cycles. Let fas ( D ) $\text{fas}(D)$ denote the minimum size of a feedback arc set in an oriented multigraph D $D$. In several papers, upper bounds for fas ( D ) $\text{fas}(D)$ were obtained for oriented multigraphs D $D$ with maximum degree upper‐bounded by a constant ...
Gregory Gutin +3 more
wiley +1 more source
On Oriented Colourings of Graphs on Surfaces
Journal of Graph Theory, EarlyView.ABSTRACT For an oriented graph G $G$, the least number of colours required to oriented colour G $G$ is called the oriented chromatic number of G $G$ and denoted χ o ( G ) ${\chi }_{o}(G)$. For a non‐negative integer g $g$ let χ o ( g ) ${\chi }_{o}(g)$ be the least integer such that χ o ( G ) ≤ χ o ( g ) ${\chi }_{o}(G)\le \unicode{x0200A}{\chi }_{o}(g)
Alexander Clow
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
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