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» Subdivisions of graphs: A generalization of paths and cycles
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DM
2008
114views more  DM 2008»
13 years 4 months ago
Subdivisions of graphs: A generalization of paths and cycles
One of the basic results in graph theory is Dirac's theorem, that every graph of order n 3 and minimum degree n/2 is Hamiltonian. This may be restated as: if a graph of ord...
Ch. Sobhan Babu, Ajit A. Diwan
CPC
2004
92views more  CPC 2004»
13 years 4 months ago
Large Topological Cliques in Graphs Without a 4-Cycle
Mader asked whether every C4-free graph G contains a subdivision of a complete graph whose order is at least linear in the average degree of G. We show that there is a subdivision...
Daniela Kühn, Deryk Osthus
DAM
2011
12 years 11 months ago
Powers of cycles, powers of paths, and distance graphs
In 1988, Golumbic and Hammer characterized powers of cycles, relating them to circular-arc graphs. We extend their results and propose several further structural characterizations ...
Min Chih Lin, Dieter Rautenbach, Francisco J. Soul...
ENDM
2007
68views more  ENDM 2007»
13 years 4 months ago
Detecting induced subgraphs
An s-graph is a graph with two kind of edges: subdivisible edges and real edges. A realisation of an s-graph B is any graph obtained by subdividing subdivisible edges of B into pa...
Benjamin Lévêque, David Y. Lin, Fr&ea...
CCCG
2008
13 years 5 months ago
Computing the Stretch Factor of Paths, Trees, and Cycles in Weighted Fixed Orientation Metrics
Let G be a graph embedded in the L1-plane. The stretch factor of G is the maximum over all pairs of distinct vertices p and q of G of the ratio LG 1 (p, q)/L1(p, q), where LG 1 (p...
Christian Wulff-Nilsen