Results 51 to 60 of about 1,265 (189)
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
A Bipartite Strengthening of the Crossing Lemma [PDF]
, 2008 The celebrated Crossing Lemma states that, in every drawing of a graph with n vertices and m geq 4n edges there are at least Omega(m^3/n^2) pairs of crossing edges; or equivalently, there is an edge that crosses Omega(m^2/n^2) other edges.
Pach, János +6 more
core +1 more source
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 +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 +5 more
wiley +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 +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 +6 more
wiley +1 more source
On Paths in a Complete Bipartite Geometric Graph
, 2001 Let A and B be two disjoint sets of points in the plane such that no three points of A ∪ B are collinear, and let n be the number of points in A. A geometric complete bipartite graph K(A, B) is a complete bipartite graph with partite sets A and B which ...
M. Kano, Atsushi Kaneko
core +1 more source
Eulerian and Even-Face Graph Partial Duals
, 2021 Eulerian and bipartite graph is a dual symmetric concept in Graph theory. It is well-known that a plane graph is Eulerian if and only if its geometric dual is bipartite.
Metrose Metsidik
core +1 more source
People and Nature, EarlyView.Abstract Protected areas represent complex social‐ecological systems that require governance and management approaches that valorise and enhance positive relationships between people and nature. This study analyses the alignment between social and ecological systems to detect the social‐ecological fit of projects focused on biodiversity conservation ...
Elena Andriollo +4 more
wiley +1 more source