Results 1 
3 of
3
An analysis of graph cut size for transductive learning
 In In proceedings of the 23rd International Conference on Machine Learning (ICML
, 2006
"... I consider the setting of transductive learning of vertex labels in graphs, in which a graph with n vertices is sampled according to some unknown distribution; there is a true labeling of the vertices such that each vertex is assigned to exactly one of k classes, but the labels of only some (r ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
I consider the setting of transductive learning of vertex labels in graphs, in which a graph with n vertices is sampled according to some unknown distribution; there is a true labeling of the vertices such that each vertex is assigned to exactly one of k classes, but the labels of only some (random) subset of the vertices are revealed to the learner.
MATCHINGS, CONNECTIVITY, AND EIGENVALUES IN REGULAR GRAPHS
, 2011
"... We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number over nvertex connected regular graphs in terms of edgeconnectedness and determine when the matching number is minimized. We also establish ..."
Abstract
 Add to MetaCart
We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number over nvertex connected regular graphs in terms of edgeconnectedness and determine when the matching number is minimized. We also establish the best upper bound for the number of cutedges over nvertex connected odd regular graphs and determine when the number of cutedges is maximized. In addition, there is a relationship between the matching number and the total domination number in regular graphs. In Chapter 3, we explore the relationship between eigenvalue and matching number in regular graphs. We give a condition on an appropriate eigenvalue that guarantees a lower bound for the matching number of a ledgeconnected dregular graph, when l ≤ d − 2. We also study what is the weakest hypothesis on the second largest eigenvalue λ2 for a dregular graph G to guarantee that G is ledgeconnected. In Chapter 4, we study several extremal problems for regular graphs, including the Chinese postman problem, the path cover number, the average edgeconnectivity, and the number of perfect matchings. In Chapter 5, we study an rdynamic coloring problem and give the relationship between the rdynamic chromatic number and the chromatic number in regular graphs. We also study rdynichromatic number of the cartesian product of paths and cycles.
Bipartite Powers of kchordal Graphs
, 2013
"... Let k be an integer and k ≥ 3. A graph G is kchordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive integer m, if G m is chordal then so is G m+2. B ..."
Abstract
 Add to MetaCart
Let k be an integer and k ≥ 3. A graph G is kchordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive integer m, if G m is chordal then so is G m+2. Brandstädt et al. in [Andreas Brandstädt, Van Bang Le, and Thomas Szymczak. Duchettype theorems for powers of HHDfree graphs. Discrete Mathematics, 177(13):916, 1997.] showed that if G m is kchordal, then so is G m+2. Powering a bipartite graph does not preserve its bipartitedness. In order to preserve the bipartitedness of a bipartite graph while powering Chandran et al. introduced the notion of bipartite powering. This notion was introduced to aid their study of boxicity of chordal bipartite graphs. The mth bipartite power G [m] of a bipartite graph G is the bipartite graph obtained from G by adding edges (u, v) where dG(u, v) is odd and less than or equal to m. Note that G [m] = G [m+1] for each odd m. In this paper we show that, given a bipartite graph G, if G is kchordal then so is G [m] , where k, m are positive integers with k ≥ 4.