An Implicit Weighted Degree Condition for Heavy Cycles in Weighted Graphs

2007 ◽  
pp. 21-29
Author(s):  
Bing Chen ◽  
Shenggui Zhang ◽  
T. C. Edwin Cheng
Keyword(s):  
Weighted Graphs ◽  
Weighted Degree ◽  
Degree Condition

scholarly journals An implicit weighted degree condition for heavy cycles

2014 ◽  
Vol 34 (4) ◽  
pp. 801
Author(s):  
Junquing Cai ◽  
Hao Li ◽  
Wantao Ning
Keyword(s):  
Weighted Degree ◽  
Degree Condition

scholarly journals Ore-type degree condition for heavy paths in weighted graphs

2005 ◽  
Vol 300 (1-3) ◽  
pp. 100-109 ◽  
Author(s):  
Hikoe Enomoto ◽  
Jun Fujisawa ◽  
Katsuhiro Ota
Keyword(s):  
Weighted Graphs ◽  
Degree Condition

scholarly journals Towards a Weighted Version of the Hajnal–Szemerédi Theorem

2013 ◽  
Vol 22 (3) ◽  
pp. 346-350 ◽  
Author(s):  
JOZSEF BALOGH ◽  
GRAEME KEMKES ◽  
CHOONGBUM LEE ◽  
STEPHEN J. YOUNG
Keyword(s):  
Positive Integer ◽  
Minimum Degree ◽  
Edge Weight ◽  
Main Question ◽  
Weighted Graphs ◽  
Lower And Upper Bounds ◽  
Weighted Degree ◽  
Weighted Version ◽  
Vertex Disjoint ◽  
The Given

For a positive integer r ≥ 2, a Kr-factor of a graph is a collection vertex-disjoint copies of Kr which covers all the vertices of the given graph. The celebrated theorem of Hajnal and Szemerédi asserts that every graph on n vertices with minimum degree at least $(1-\frac{1}{r})n contains a Kr-factor. In this note, we propose investigating the relation between minimum degree and existence of perfect Kr-packing for edge-weighted graphs. The main question we study is the following. Suppose that a positive integer r ≥ 2 and a real t ∈ [0, 1] is given. What is the minimum weighted degree of Kn that guarantees the existence of a Kr-factor such that every factor has total edge weight at least $$t\binom{r}{2}$?$ We provide some lower and upper bounds and make a conjecture on the asymptotics of the threshold as n goes to infinity.

scholarly journals Heavy cycles in k-connected weighted graphs with large weighted degree sums

2008 ◽  
Vol 308 (20) ◽  
pp. 4531-4543 ◽  
Author(s):  
Bing Chen ◽  
Shenggui Zhang ◽  
T.C. Edwin Cheng
Keyword(s):  
Weighted Graphs ◽  
Weighted Degree

EM Algorithm Based on Fuzzification and its Application

2012 ◽  
Vol 532-533 ◽  
pp. 1445-1449
Author(s):  
Ting Ting Tong ◽  
Zhen Hua Wu
Keyword(s):  
Em Algorithm ◽  
Mixed Model ◽  
Image Data ◽  
Training Sample ◽  
Model Parameters ◽  
Parameter Learning ◽  
Weighted Degree ◽  
The Em Algorithm ◽  
The Impact

EM algorithm is a common method to solve mixed model parameters in statistical classification of remote sensing image. The EM algorithm based on fuzzification is presented in this paper to use a fuzzy set to represent each training sample. Via the weighted degree of membership, different samples will be of different effect during iteration to decrease the impact of noise on parameter learning and to increase the convergence rate of algorithm. The function and accuracy of classification of image data can be completed preferably.

Heat Kernel Estimates on Weighted Graphs

2000 ◽  
Vol 32 (4) ◽  
pp. 477-483 ◽  
Author(s):  
Bernd Metzger ◽  
Peter Stollmann
Keyword(s):  
Heat Kernel ◽  
Weighted Graphs ◽  
Kernel Estimates ◽  
Heat Kernel Estimates

scholarly journals Path ideals of weighted graphs

2015 ◽  
Vol 219 (9) ◽  
pp. 3889-3912 ◽  
Author(s):  
Bethany Kubik ◽  
Sean Sather-Wagstaff
Keyword(s):  
Weighted Graphs

scholarly journals Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

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