Results 91 to 100 of about 5,057 (262)
A Coarse Geometric Approach to Graph Layout Problems
Journal of Graph Theory, EarlyView.ABSTRACT We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are ...
Wanying Huang +3 more
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
Induced Subgraphs With Many Distinct Degrees [PDF]
Combinatorics, Probability and Computing, 2017 Let hom(G) denote the size of the largest clique or independent set of a graphG. In 2007, Bukh and Sudakov proved that everyn-vertex graphGwith hom(G) =O(logn) contains an induced subgraph with Ω(n1/2) distinct degrees, and raised the question of deciding whether an analogous result holds for everyn-vertex graphGwith hom(G) =O(nϵ), whereϵ> 0 is a ...
Bhargav P. Narayanan, István Tomon
openaire +3 more sources
On the Hardness of Switching to a Small Number of Edges
Journal of Graph Theory, EarlyView.ABSTRACT Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non‐adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching‐equivalent if one can be made isomorphic to the other one by a sequence of switches. Jelínková et al. [DMTCS 13, no. 2, 2011]
Vít Jelínek +2 more
wiley +1 more source
The four-in-a-tree problem in triangle-free graphs [PDF]
The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time O(n4) whether three given vertices of a graph belong to an induced tree. Here, we study four-in-a-tree for triangle-free graphs. We give a structural answer to the following question
Nicolas Trotignon +2 more
core
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
On Strongly Regular Graphs and the Friendship Theorem
MathematicsThis paper presents an alternative proof of the celebrated friendship theorem, originally established by Erdős, Rényi, and Sós in 1966. The proof relies on a closed-form expression for the Lovász ϑ-function of strongly regular graphs, recently derived by
Igal Sason
doaj +1 more source
Search Result Clustering via Randomized Partitioning of Query-Induced Subgraphs [PDF]
Telfor Journal, 2009 In this paper, we present an approach to search result clustering, using partitioning of underlying link graph. We define the notion of "query-induced subgraph" and formulate the problem of search result clustering as a problem of efficient partitioning ...
A. Bradic
doaj
On graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph [PDF]
We prove a decomposition theorem for graphs that do not contain a subdivision of the complete graph on four vertices as an induced subgraph.Induced, subgraph, decomposition.
Nicolas Trotignon +2 more
core
Maximum regular induced subgraphs in -free graphs
, 2012 Finding maximum regular induced subgraphs is a family of algorithmic graph problems containing several important representatives such as maximum independent set, maximum clique, and maximum induced matching. These problems are generally NP-hard.
Lozin, Vadim V., Mosca, Raffaele
core +1 more source