Results 1 to 10 of about 1,232,989 (193)
Partial Steiner Triple Systems With an Almost Parallel Class Missing Any Given Point
Journal of Combinatorial Designs, EarlyView.ABSTRACT We say that a hypergraph is factor critical if it has no 1‐factor but deletion of any vertex results in a hypergraph that has a 1‐factor. We show that any factor‐critical hypergraph of order n $n$ has at least n $n$ edges, and that for all integers k > 1 $k\gt 1$ and n > 1 $n\gt 1$ with n ≡ 1 ( mod k ) $n\equiv 1({\rm{mod}}\,k)$ there exists a
Darryn Bryant +2 more
wiley +1 more source
Catalan Bounds for Symmetric Strength‐Two Orthogonal Arrays
Journal of Combinatorial Designs, EarlyView.ABSTRACT A Hamming shell construction is a two‐level array obtained by taking every binary vector of a given Hamming weight a prescribed number of times, for each weight in turn. Such arrays are invariant under all permutations of the factors, and they are strength‐two orthogonal arrays exactly when the multiplicities satisfy three linear constraints ...
Ruwan C. Karunanayaka
wiley +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
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
The 1 3 $\frac{1}{3}$‐Conjectures for Domination in Cubic Graphs
Journal of Graph Theory, EarlyView.ABSTRACT A set S $S$ of vertices in a graph G $G$ is a dominating set of G $G$ if every vertex not in S $S$ is adjacent to a vertex in S $S$. The domination number of G $G$, denoted by γ ( G ) $\gamma (G)$, is the minimum cardinality among all dominating sets in G $G$. In a breakthrough paper in 2008, Löwenstein and Rautenbach proved that if G $G$ is a
Paul Dorbec, Michael A. Henning
wiley +1 more source
Against All Odds?—A Surprisingly Not So Easy Dice Game
Teaching Statistics, EarlyView.ABSTRACT A game with 11 players, 2 dice, and simple rules. However, it turns out that the best strategy is not only absent from the literature, but that misconceptions about winning strategies also prevail among surveyed students. This makes it all the more surprising that it is not so easy to get to the bottom of the game mathematically.
Christoph Oberbucher +1 more
wiley +1 more source
On the Limits of Intransitive Coordination
Ratio, EarlyView.ABSTRACT A growing number of authors suggest that concept coordination—the kind of relation we pick out when we say that the concepts of one or more individuals represent something as the same—is not a transitive relation. Here we consider global features of representational systems to break new ground in the assessment of the intransitivity view. From
Víctor M. Verdejo, Joost J. Joosten
wiley +1 more source
Evaluating Large‐Language Models in Bioinformatics Applications
Advanced Computing, Volume 1, Issue 1, December 2026.This work systematically evaluates advanced large language models across six representative bioinformatics tasks, from drug–drug interaction prediction and molecular optimization to single‐cell annotation and computational biology problem solving. The benchmark quantifies both their promise and limitations, offering practical guidance for prompt design,
Hengchuang Yin +9 more
wiley +1 more source
Mixed Steiner Triple Systems With Shortest Length
Journal of Combinatorial Designs, Volume 34, Issue 12, Page 533-544, December 2026.ABSTRACT A mixed Steiner triple system is a 3‐GDD which is viewed as a code with minimum Hamming distance 3. These codes are the minimum weight codewords of a 1‐perfect code over a mixed alphabet, when the related codes exist, and provide the connection between 3‐GDDs and coding theory.
Tuvi Etzion
wiley +1 more source
Characterizing Pyramidal Hadamard Designs With the Largest Number of Fixed Points
Journal of Combinatorial Designs, Volume 34, Issue 12, Page 569-573, December 2026.ABSTRACT A symmetric ( v , k , λ )‐design is said to be f‐pyramidal, with f < v − 1, under the action of a group G if G acts as an automorphism group fixing f points and acting sharply transitively on the remaining ones. We show that, necessarily, f ≤ v − 2 ( k − λ ). In particular, for a Hadamard design with parameters ( v , k , λ ) = ( 4 m − 1 , 2 m −
Tommaso Traetta
wiley +1 more source