Results 221 to 230 of about 249,936 (334)

On Strongly and Robustly Critical Graphs

open access: yesJournal 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

open access: yesJournal 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

Is the Matrix Completion of Reduced Density Matrices Unique? [PDF]

open access: yesJ Phys Chem Lett
Massaccesi GE   +6 more
europepmc   +1 more source

Tight Bounds for Hypercube Minor‐Universality

open access: yesJournal 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

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