Results 1 to 10 of about 213,970 (327)
Treewidth 2 in the Planar Graph Product Structure Theorem [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any
Marc Distel +4 more
doaj +1 more source
A Polynomial-time Algorithm for Outerplanar Diameter Improvement
, 2014 The Outerplanar Diameter Improvement problem asks, given a graph $G$ and an integer $D$, whether it is possible to add edges to $G$ in a way that the resulting graph is outerplanar and has diameter at most $D$.
Cohen, Nathann +6 more
core +3 more sources
On Computation of Degree-Based Entropy of Planar Octahedron Networks
Journal of Function Spaces, 2022 Chemical graph theory is the combination of mathematical graph theory and chemistry. To analyze the biocompatibility of the compounds, topological indices are used in the research of QSAR/QSPR studies.
Tian-Le Sun +5 more
doaj +1 more source
Near-colorings: non-colorable graphs and NP-completeness [PDF]
, 2013 A graph G is (d_1,..,d_l)-colorable if the vertex set of G can be partitioned into subsets V_1,..,V_l such that the graph G[V_i] induced by the vertices of V_i has maximum degree at most d_i for all 1
Montassier, Mickael, Ochem, Pascal
core
The Weisfeiler-Leman Dimension of Planar Graphs is at most 3
, 2017 We prove that the Weisfeiler-Leman (WL) dimension of the class of all finite planar graphs is at most 3. In particular, every finite planar graph is definable in first-order logic with counting using at most 4 variables.
Kiefer, Sandra +2 more
core +1 more source
Transfer-Efficient Face Routing Using the Planar Graphs of Neighbors in High Density WSNs
Sensors, 2017 Face routing has been adopted in wireless sensor networks (WSNs) where topological changes occur frequently or maintaining full network information is difficult.
Eun-Seok Cho, Yongbin Yim, Sang-Ha Kim
doaj +1 more source
Homomorphisms of planar signed graphs to signed projective cubes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1.
Reza Naserasr +2 more
doaj +1 more source
A Planarity Test via Construction Sequences
, 2012 Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests.
A.K. Kelmans +20 more
core +2 more sources
Bar 1-Visibility Graphs and their relation to other Nearly Planar Graphs [PDF]
, 2013 A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp.
Evans, William +5 more
core
, 2017 We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer $k$-planar graphs, where each edge is crossed by at
AWM Dress +23 more
core +1 more source