Results 21 to 30 of about 167 (120)

Fractional List Packing for Layered Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT The fractional list packing number χ ℓ • ( G ) ${\chi }_{\ell }^{\bullet }(G)$ of a graph G $G$ is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment L : V ( G ) → 2 N $L:V(G)\to {2}^{{\mathbb{N}}}$ need to be to ensure the existence of a “perfectly ...
Stijn Cambie, Wouter Cames van Batenburg
wiley   +1 more source

Orientations of Graphs With at Most One Directed Path Between Every Pair of Vertices

Journal of Graph Theory, EarlyView.
ABSTRACT Given a graph G $G$, we say that an orientation D $D$ of G $G$ is a KT orientation if, for all u , v ∈ V ( D ) $u,v\in V(D)$, there is at most one directed path (in any direction) between u $u$ and v $v$. Graphs that admit such orientations have been used to construct graphs with large chromatic number and small clique number that served as ...
Barbora Dohnalová, Jiří Kalvoda, Gaurav Kucheriya, Sophie Spirkl   +3 more
wiley   +1 more source

Stable Cuts, NAC‐Colourings and Flexible Realisations of Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT A (2‐dimensional) realisation of a graph G $G$ is a pair ( G , p ) $(G,p)$, where p $p$ maps the vertices of G $G$ to R 2 ${{\mathbb{R}}}^{2}$. A realisation is flexible if it can be continuously deformed while keeping the edge lengths fixed, and rigid otherwise.
Katie Clinch, Dániel Garamvölgyi, John Haslegrave, Tony Huynh, Jan Legerský, Anthony Nixon   +5 more
wiley   +1 more source

Cell rotation graphs of strongly connected orientations of plane graphs with an application

, 2003
The cell rotation graph D(G) on the strongly connected orientations of a 2-edge-connected plane graph G is defined. It is shown that D(G) is a directed forest and every component is an in-tree with one root; if T is a component of D(G), the reversions of
Lam, Peter Che Bor, Peter Che Bor Lam, Wai Chee Shiu, Zhang, Heping, Heping Zhang, Shiu, Wai Chee   +5 more
core   +1 more source

Linear Versus Centred Colouring via Pseudogrids

Journal of Graph Theory, EarlyView.
ABSTRACT A centred colouring of a graph is a vertex colouring in which every connected subgraph contains a vertex whose colour is unique and a linear colouring is a vertex colouring in which every (not‐necessarily induced) path contains a vertex whose colour is unique. For a graph G $G$, the centred chromatic number χ cen ( G ) ${\chi }_{\text{cen}}(G)$
Prosenjit Bose, Vida Dujmović, Hussein Houdrouge, Mehrnoosh Javarsineh, Pat Morin   +4 more
wiley   +1 more source

Allocation of Indivisible Items With a Common Preference Graph: Minimizing Total Dissatisfaction

Networks, EarlyView.
ABSTRACT Allocating indivisible items among a set of agents is a frequently studied discrete optimization problem. In the setting considered in this work, the agents' preferences over the items are assumed to be identical. We consider a very recent measure for the overall quality of an allocation which does not rely on numerical valuations of the items.
Nina Chiarelli, Clément Dallard, Andreas Darmann, Stefan Lendl, Martin Milanič, Peter Muršič, Ulrich Pferschy   +6 more
wiley   +1 more source

Contentment in graph theory: Covering graphs with cliques

, 1977
Fundamental questions posed by Boole in 1868 on the theory of sets have in recent years been translated to problems in graph theory. The major problems that this paper deals with are determining the minimum number of complete subgraphs of graph G which ...
Orlin, James
core   +1 more source

Identifiability conditions in cognitive diagnosis: Implications for Q‐matrix estimation algorithms

British Journal of Mathematical and Statistical Psychology, EarlyView.
Abstract The Q‐matrix of a cognitively diagnostic assessment (CDA), documenting the item‐attribute associations, is a key component of any CDA. However, the true Q‐matrix underlying a CDA is never known and must be estimated—typically by content experts.
Hyunjoo Kim, Hans Friedrich Köhn, Chia‐Yi Chiu   +2 more
wiley   +1 more source

Story2Board: A Training‐Free Approach for Expressive Visual Storytelling

Computer Graphics Forum, EarlyView.
Abstract We present Story2Board, a training‐free framework for expressive storyboard generation from natural language. Existing methods narrowly focus on subject identity, overlooking key aspects of visual storytelling such as spatial composition, background evolution, and narrative pacing.
D. Dinkevich, M. Levy, O. Avrahami, D. Samuel, D. Lischinski   +4 more
wiley   +1 more source

Distances in planar graphs

, 2022
In graph theory, the degree diameter problem asks for the maximum number of vertices a graph with given maximum degree and diameter can have. The face-degree of a face in plane graph is the length of the shortest closed walk traversing the boundary of ...
Du Preez, Brandon
core