Results 1 to 10 of about 1,232,917 (141)

Mixed Steiner Triple Systems With Shortest Length

Journal of Combinatorial Designs, EarlyView.
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

Exact Values and Bounds on Covering Schemes of Strength Two

Journal of Combinatorial Designs, EarlyView.
ABSTRACT In this work, we investigate covering schemes of strength 2 over finite abelian groups, establishing new lower and upper bounds and evaluating new exact values. A main result is a new general lower bound that improves the trivial one and achieves optimality for the binary case. We also develop a recursive relation based on subsets of the group
André G. Castoldi, Anderson N. Martinhão, Emerson L. Monte Carmelo, Pablo H. Perondi, Otávio J. N. T. N. dos Santos   +4 more
wiley   +1 more source

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, Sara Davies, Jack Neubecker   +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

On Fork‐Free t‐Perfect Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT In an effort to understand the complexity of the maximum independent set problem, Chvátal introduced t‐perfect graphs. While a full characterization of this class remains open, important progress has been made for claw‐free graphs [Bruhn and Stein, Math. Program. 2012] and P 5 ${P}_{5}$‐free graphs [Bruhn and Fuchs, SIAM J. Discrete Math. 2017]
Yixin Cao, Shenghua Wang
wiley   +1 more source

Tree Independence Number III. Thetas, Prisms and Stars

Journal of Graph Theory, EarlyView.
ABSTRACT We prove that for every t ∈ N $t\in {\mathbb{N}}$ there exists τ = τ ( t ) ∈ N $\tau =\tau (t)\in {\mathbb{N}}$ such that every (theta, prism, K 1 , t ${K}_{1,t}$)‐free graph has tree independence number at most τ $\tau $ (where we allow “prisms” to have one path of length zero).
Maria Chudnovsky, Sepehr Hajebi, Nicolas Trotignon   +2 more
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, Ilkyoo Choi, Boram Park, Mark Siggers   +3 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