Results 1 to 10 of about 3,599,893 (267)
Matching book thickness of generalized Petersen graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2022 Summary: The matching book embedding of a graph \(G\) is to place its vertices on the spine, and arrange its edges on the pages so that the edges in the same page do not intersect each other and the edges induced subgraphs of each page are 1-regular.
Zeling Shao, Huiru Geng, Zhiguo Li
semanticscholar +6 more sources
On the Book Thickness of k-Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Graphs and Algorithms Every k-tree has book thickness at most k + 1, and this bound is best possible for all k \textgreater= 3. Vandenbussche et al. [SIAM J. Discrete Math., 2009] proved that every k-tree that has a smooth degree-3 tree decomposition with width k has book thickness at most k.
Vida Dujmović, David R. Wood
semanticscholar +7 more sources
On the Upward Book Thickness Problem: Combinatorial and Complexity Results [PDF]
European Journal of Combinatorics, 2021 Appears in the Proceedings of the 29th International Symposium on Graph Drawing and Network Visualization (GD 2021)
Sujoy Bhore +3 more
semanticscholar +8 more sources
The Book Thickness of 1-Planar Graphs is Constant [PDF]
Algorithmica, 2016 In a book embedding, the vertices of a graph are placed on the spine of a book and the edges are assigned to pages, so that edges on the same page do not cross. In this paper, we prove that every $1$-planar graph (that is, a graph that can be drawn on the plane such that no edge is crossed more than once) admits an embedding in a book with constant ...
Michael A. Bekos +3 more
semanticscholar +7 more sources
Star arboricity relaxed book thickness of $K_n$ [PDF]
arXiv.orgA book embedding of the complete graph $K_n$ needs $\lceil \frac{n}{2} \rceil$ pages and the page-subgraphs can be chosen to be spanning paths (for $n$ even) and one spanning star for $n$ odd. We show that all page-subgraphs can be chosen to be {\rm star forests} by including one extra {\rm cross-cap} page or two new ordinary pages.
Paul C. Kainen
semanticscholar +4 more sources
Genus and book thickness of reduced cozero-divisor graphs of commutative rings
Revista de la Unión Matemática ArgentinaSummary: For a commutative ring \(R\) with identity, let \(\langle a\rangle\) be the principal ideal generated by \(a\in R\). Let \(\Omega (R)^*\) be the set of all nonzero proper principal ideals of \(R\). The reduced cozero-divisor graph \(\Gamma_r (R)\) of \(R\) is the simple undirected graph whose vertex set is \(\Omega (R)^*\) and such that two ...
E. Jesili +2 more
semanticscholar +3 more sources
Matching Book Thickness of Halin Graphs [PDF]
, 2020 The proof in the manuscripts can be ...
Zeling Shao, Huiru Geng, Zhiguo Li
core +4 more sources
Book thickness of the non-zero component union graph of the finite dimensional vector space
Indian Journal of Pure and Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
N. Mohamed Rilwan, S. Vasanthi Devi
semanticscholar +3 more sources
Book Thickness of Planar Zero Divisor Graphs [PDF]
Missouri Journal of Mathematical Sciences, 2015 Let $R$ be a finite commutative ring with identity. We form the zero divisor graph of $R$ by taking the nonzero zero divisors as the vertices and connecting two vertices, $x$ and $y$, by an edge if and only if $xy=0$. We establish that if the zero divisor graph of a finite commutative ring with identity is planar, then the graph has a planar supergraph
Thomas C. McKenzie, Shannon Overbay
semanticscholar +4 more sources
Journal of Combinatorial Theory, Series B, 1979 AbstractThe book thickness bt(G) of a graph G is defined, its basic properties are delineated, and relations are given with other invariants such as thickness, genus, and chromatic number. A graph G has book thickness bt(G) ≤ 2 if and only if it is a subgraph of a hamiltonian planar graph, but we conjecture that there are planar graphs with arbitrarily
Frank R. Bernhart, Paul C. Kainen
semanticscholar +4 more sources