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» Bounds of Graph Characteristics
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DM
2008
110views more  DM 2008»
13 years 7 months ago
Nonrepetitive colorings of graphs of bounded tree-width
A sequence of the form s1s2 . . . sms1s2 . . . sm is called a repetition. A vertex-coloring of a graph is called nonrepetitive if none of its paths is repetitively colored. We ans...
André Kündgen, Michael J. Pelsmajer
JGT
2007
99views more  JGT 2007»
13 years 7 months ago
The upper bound of the number of cycles in a 2-factor of a line graph
Let G be a simple graph with order n and minimum degree at least two. In this paper, we prove that if every odd branch-bond in G has an edge-branch, then its line graph has a 2-fa...
Jun Fujisawa, Liming Xiong, Kiyoshi Yoshimoto, She...
DMTCS
2010
133views Mathematics» more  DMTCS 2010»
13 years 5 months ago
An improved bound on the largest induced forests for triangle-free planar graphs
We proved that every planar triangle-free graph with n vertices has a subset of vertices that induces a forest of size at least (71n + 72)/128. This improves the earlier work of S...
Lukasz Kowalik, Borut Luzar, Riste Skrekovski
COMBINATORICS
2006
124views more  COMBINATORICS 2006»
13 years 7 months ago
Bounded-Degree Graphs have Arbitrarily Large Geometric Thickness
Abstract. The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppste...
János Barát, Jirí Matousek, D...
CN
2006
70views more  CN 2006»
13 years 7 months ago
Small-world characteristics of Internet topologies and implications on multicast scaling
Recent work has shown that the physical connectivity of the Internet exhibits small-world behavior. Characterizing such behavior is important not only for generating realistic Int...
Shudong Jin, Azer Bestavros