Cycles and rays
Geňa Hahn,Gert Sabidussi,Robert E. Woodrow,Rays: Basic Structures in Finite,Infinite Graphs +4 more
- 01 Jan 1990
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TL;DR: Hilton and Rodger as mentioned in this paper considered the problem of infinite versions of Menger and Gallai-Milgram Theorems for Ordered Sets and Graphs and proposed a solution to it.
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Abstract: Linkability in Countable-Like Webs.- Decomposition into Cycles I: Hamilton Decompositions.- An Order- and Graph- Theoretical Characterisation of Weakly Compact Cardinals.- Small Cycle Double Covers of Graphs.- ?-Transformations, Local Complementations and Switching.- Two Extremal Problems in Infinite Ordered Sets and Graphs: Infinite Versions of Menger and Gallai-Milgram Theorems for Ordered Sets and Graphs.- Chvatal-Erd?s Theorem for Digraphs.- Long Cycles and the Codiameter of a Graph II.- Compatible Euler Tours in Eulerian Digraphs.- A.J.W. Hilton, C.A. Rodger, Edge-Colouring Graphs and Embedding Partial Triple Systems of Even Index.- On the Rank of Fixed Point Sets of Automorphisms of Free Groups.- On Transition Polynomials of 4-Regular Graphs.- On Infinite n-Connected Graphs.- Ordered Graphs Without Infinite Paths.- Ends of Infinite Graphs, Potential Theory and Electrical Networks.- Topological Aspects of Infinite Graphs.- Dendroids, End-Separators, and Almost Circuit-Connected Trees.- Partition Theorems for Graphs Respecting the Chromatic Number.- Vertex-Transitive Graphs That Are Not Cayley Graphs.
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Citations
Circuit double cover of graphs
Cun-Quan Zhang
- 01 Apr 2012
TL;DR: The circuit double cover conjecture (CDC conjecture) is considered by most graph theorists as one of the major open problems in the field of graph theory as discussed by the authors, and it has been studied extensively.
Tree amalgamation of graphs and tessellations of the Cantor sphere
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Evaluations of Topological Tutte Polynomials
TL;DR: A reduction formula is presented for the transition polynomial of the tensor product of two embedded graphs, showing that it leads to additional relations among these polynomials and to further combinatorial interpretations of P(G) and R(G).
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The Chvátal-Erdos condition for cycles in triangle-free graphs
TL;DR: It is proved that if G is a triangle-free graph with v vertices whose independence number does not exceed its connectivity then G has cycles of every length n for 4 ⩽ n⩽ v ( G ) unless G = K v / 2, v /2 or G isA 5-cycle.
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Eulerian tour algorithms for data visualization and the PairViz package
TL;DR: PairViz is an R package that produces orderings of statistical objects for visualization purposes that implements various edge traversal algorithms which are based on Eulerian tours and Hamiltonian decompositions, and their application to two visualization problems.