scholarly journals Compression via Matroids: A Randomized Polynomial Kernel for Odd Cycle Transversal

Author(s):  
Stefan Kratsch ◽  
Magnus Wahlström
Keyword(s):  
2021 ◽  
Vol 35 (4) ◽  
pp. 2387-2429
Author(s):  
Bart M. P. Jansen ◽  
Marcin L. Pilipczuk ◽  
Erik Jan van Leeuwen

Author(s):  
Hedieh Sajedi ◽  
Mehran Bahador

In this paper, a new approach for segmentation and recognition of Persian handwritten numbers is presented. This method utilizes the framing feature technique in combination with outer profile feature that we named this the adapted framing feature. In our proposed approach, segmentation of the numbers into digits has been carried out automatically. In the classification stage of the proposed method, Support Vector Machines (SVM) and k-Nearest Neighbors (k-NN) are used. Experimentations are conducted on the IFHCDB database consisting 17,740 numeral images and HODA database consisting 102,352 numeral images. In isolated digit level on IFHCDB, the recognition rate of 99.27%, is achieved by using SVM with polynomial kernel. Furthermore, in isolated digit level on HODA, the recognition rate of 99.07% is achieved by using SVM with polynomial kernel. The experiments illustrate that applying our proposed method resulted higher accuracy compared to previous researches.


Author(s):  
Agnes D. Garciano ◽  
Maria Czarina T. Lagura ◽  
Reginaldo M. Marcelo

For a simple connected graph [Formula: see text] let [Formula: see text] be a coloring of [Formula: see text] where two adjacent vertices may be assigned the same color. Let [Formula: see text] be the sum of colors of neighbors of any vertex [Formula: see text] The coloring [Formula: see text] is a sigma coloring of [Formula: see text] if for any two adjacent vertices [Formula: see text] [Formula: see text] The least number of colors required in a sigma coloring of [Formula: see text] is the sigma chromatic number of [Formula: see text] and is denoted by [Formula: see text] A sigma coloring of a graph is a neighbor-distinguishing type of coloring and it is known that the sigma chromatic number of a graph is bounded above by its chromatic number. It is also known that for a path [Formula: see text] and a cycle [Formula: see text] where [Formula: see text] [Formula: see text] and [Formula: see text] if [Formula: see text] is even. Let [Formula: see text] the join of the graphs [Formula: see text], where [Formula: see text] or [Formula: see text] [Formula: see text] and [Formula: see text] is not an odd cycle for any [Formula: see text]. It has been shown that if [Formula: see text] for [Formula: see text] and [Formula: see text] then [Formula: see text]. In this study, we give necessary and sufficient conditions under which [Formula: see text] where [Formula: see text] is the join of copies of [Formula: see text] and/or [Formula: see text] for the same value of [Formula: see text]. Let [Formula: see text] and [Formula: see text] be positive integers with [Formula: see text] and [Formula: see text] In this paper, we show that [Formula: see text] if and only if [Formula: see text] or [Formula: see text] is odd, [Formula: see text] is even and [Formula: see text]; and [Formula: see text] if and only if [Formula: see text] is even and [Formula: see text] We also obtain necessary and sufficient conditions on [Formula: see text] and [Formula: see text], so that [Formula: see text] for [Formula: see text] where [Formula: see text] or [Formula: see text] other than the cases [Formula: see text] and [Formula: see text]


2019 ◽  
Vol 18 (10) ◽  
pp. 1950184 ◽  
Author(s):  
Mike Janssen ◽  
Thomas Kamp ◽  
Jason Vander Woude

Given a nontrivial homogeneous ideal [Formula: see text], a problem of great recent interest has been the comparison of the [Formula: see text]th ordinary power of [Formula: see text] and the [Formula: see text]th symbolic power [Formula: see text]. This comparison has been undertaken directly via an exploration of which exponents [Formula: see text] and [Formula: see text] guarantee the subset containment [Formula: see text] and asymptotically via a computation of the resurgence [Formula: see text], a number for which any [Formula: see text] guarantees [Formula: see text]. Recently, a third quantity, the symbolic defect, was introduced; as [Formula: see text], the symbolic defect is the minimal number of generators required to add to [Formula: see text] in order to get [Formula: see text]. We consider these various means of comparison when [Formula: see text] is the edge ideal of certain graphs by describing an ideal [Formula: see text] for which [Formula: see text]. When [Formula: see text] is the edge ideal of an odd cycle, our description of the structure of [Formula: see text] yields solutions to both the direct and asymptotic containment questions, as well as a partial computation of the sequence of symbolic defects.


2013 ◽  
Vol 53 (4) ◽  
pp. 609-620 ◽  
Author(s):  
Pranabendu Misra ◽  
Venkatesh Raman ◽  
M. S. Ramanujan ◽  
Saket Saurabh

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