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SIROCCO
2007
15 years 7 months ago
Fast Periodic Graph Exploration with Constant Memory
We consider the problem of periodic exploration of all nodes in undirected graphs by using a nite state automaton called later a robot. The robot, using a constant number of state...
Leszek Gasieniec, Ralf Klasing, Russell A. Martin,...
DM
2006
92views more  DM 2006»
15 years 6 months ago
Sums of powers of the degrees of a graph
For a graph G and k a real number, we consider the sum of the k-th powers of the degrees of the vertices of G. We present some general bounds on this sum for various values of k. ...
Sebastian M. Cioaba
CORR
2007
Springer
113views Education» more  CORR 2007»
15 years 6 months ago
Note on edge-colored graphs and digraphs without properly colored cycles
We study the following two functions: d(n, c) and d(n, c); d(n, c) (d(n, c)) is the minimum number k such that every c-edge-colored undirected (directed) graph of order n and mini...
Gregory Gutin
JCT
2008
96views more  JCT 2008»
15 years 6 months ago
Graphs with full rank 3-color matrix and few 3-colorings
We exhibit a a counterexample to a conjecture of Thomassen stating that the number of distinct 3-colorings of every graph whose 3color matrix has full column rank is superpolynomi...
Serguei Norine, Jean-Sébastien Sereni
JCT
2010
70views more  JCT 2010»
15 years 4 months ago
Graphs with bounded tree-width and large odd-girth are almost bipartite
We prove that for every k and every ε > 0, there exists g such that every graph with tree-width at most k and odd-girth at least g has circular chromatic number at most 2 + ε...
Alexandr V. Kostochka, Daniel Král', Jean-S...