Results 121 to 130 of about 27,298 (312)

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

The Parameterized Complexity of the Rainbow Subgraph Problem

Algorithms, 2015
The NP-hard RAINBOW SUBGRAPH problem, motivated from bioinformatics, is to find in an edge-colored graph a subgraph that contains each edge color exactly once and has at most \(k\) vertices.
Falk Hüffner, Christian Komusiewicz, Rolf Niedermeier, Martin Rötzschke   +3 more
doaj   +1 more source

On a Clique‐Building Game of Erdős

Journal of Graph Theory, EarlyView.
ABSTRACT The following game was introduced in a list of open problems from 1983 attributed to Erdős: two players take turns claiming edges of a Kn ${K}_{n}$ until all edges are exhausted. Player 1 wins the game if the largest clique that they claim at the end is strictly larger than the largest clique of their opponent; otherwise, Player 2 wins the ...
Alexandru Malekshahian, Sam Spiro
wiley   +1 more source

Analysis of size of the largest dense subgraph of random hypergraph

Труды Института системного программирования РАН, 2018
Random networks are often described using Erdos-Renyi model of random graph . The concept of graph density is often used in random network analysis.
N. N. Kuzyrin, D. O. Lazarev
doaj   +1 more source

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, Eva Jelínková, Jan Kratochvíl   +2 more
wiley   +1 more source

Layered Subgraphs of the Hypercube

The Electronic Journal of Combinatorics
A subgraph of the $n$-dimensional hypercube is called 'layered' if it is a subgraph of a layer of some hypercube. In this paper we show that there exist subgraphs of the cube of arbitrarily large girth that are not layered. This answers a question of Axenovich, Martin and Winter. Perhaps surprisingly, these subgraphs may even be taken to be induced.
Natalie C. Behague, Imre Leader, Natasha Morrison, Kada Williams   +3 more
openaire   +3 more sources

Neural Subgraph Isomorphism Counting

, 2020
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and ...
Jiang, Xin, Haojie Pan, He, Mutian, Xin Jiang, Shang, Lifeng, Lifeng Shang, Pan, Haojie, Song, Yangqiu, Xin Liu, Mutian He, Liu, Xin, Yangqiu Song   +11 more
core   +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

Weak Degeneracy of Planar Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT The weak degeneracy of a graph G $G$ is a numerical parameter that was recently introduced by the first two authors with the aim of understanding the power of greedy algorithms for graph coloring. Every d $d$‐degenerate graph is weakly d $d$‐degenerate, but the converse is not true in general (e.g., all connected d $d$‐regular graphs except ...
Anton Bernshteyn, Eugene Lee, Evelyne Smith‐Roberge   +2 more
wiley   +1 more source

Explainable Neural Subgraph Matching With Learnable Multi-Hop Attention

Subgraph matching is a challenging problem with a wide range of applications in drug discovery, social network analysis, biochemistry, and cognitive science.
Thanh Toan Nguyen, Tho T. Quan, Jo, J, Poux, F, Duc Q. Nguyen, Anirban, S, Quan, TT, Nguyen, DQ, Nguyen, TT, Jun Jo, Shikha Anirban, Florent Poux   +11 more
core   +1 more source