A characterization of the subcubic graphs achieving equality in the Haxell‐Scott lower bound for the matching number

2020 ◽  
Author(s):  
Michael A. Henning ◽  
Zekhaya B. Shozi
Keyword(s):  
Lower Bound ◽  
Matching Number ◽  
Subcubic Graphs

scholarly journals A lower bound on the acyclic matching number of subcubic graphs

2018 ◽  
Vol 341 (8) ◽  
pp. 2353-2358 ◽  
Author(s):  
M. Fürst ◽  
D. Rautenbach
Keyword(s):  
Lower Bound ◽  
Matching Number ◽  
Subcubic Graphs ◽  
Acyclic Matching

Some results involving HNBUE distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1038-1044
Author(s):  
A. P. Basu ◽  
S. N. U. A. Kirmani
Keyword(s):  
Lower Bound ◽  
Exponential Distribution ◽  
Renewal Process ◽  
Renewal Function ◽  
Underlying Distribution

A characterization of the exponential distribution in the class of all distributions which are HNBUE or HNWUE is proved. An upper (a lower) bound is obtained on the renewal function of a renewal process when the underlying distribution is HNBUE (HNWUE).

scholarly journals Heuristic for estimation of multiqubit genuine multipartite entanglement

2015 ◽  
Vol 13 (03) ◽  
pp. 1550023 ◽  
Author(s):  
Paulo E. M. F. Mendonça ◽  
Marcelo A. Marchiolli ◽  
Gerard J. Milburn
Keyword(s):  
Lower Bound ◽  
Density Matrix ◽  
Lower Bounds ◽  
Multipartite Entanglement ◽  
Zero Temperature ◽  
Mixed States ◽  
X State ◽  
Computational Basis ◽  
Genuine Multipartite Entanglement

For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature.

scholarly journals MINIMAL NON-INTEGER ALPHABETS ALLOWING PARALLEL ADDITION

2018 ◽  
Vol 58 (5) ◽  
pp. 285 ◽  
Author(s):  
Jan Legerský
Keyword(s):  
Lower Bound ◽  
Necessary Conditions ◽  
Parallel Addition ◽  
Consecutive Integers ◽  
Numeration Systems

Parallel addition, i.e., addition with limited carry propagation has been so far studied for complex bases and integer alphabets. We focus on alphabets consisting of integer combinations of powers of the base. We give necessary conditions on the alphabet allowing parallel addition. Under certain assumptions, we prove the same lower bound on the size of the generalized alphabet that is known for alphabets consisting of consecutive integers. We also extend the characterization of bases allowing parallel addition to numeration systems with non-integer alphabets.

scholarly journals Semiarcs with Long Secants

10.37236/3771 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Bence Csajbók
Keyword(s):  
Lower Bound ◽  
Projective Plane ◽  
Complete Characterization ◽  
Symmetric Difference ◽  
Blocking Set ◽  
Point Set

In a projective plane $\Pi_q$ of order $q$, a non-empty point set $\mathcal{S}_t$ is a $t$-semiarc if the number of tangent lines to $\mathcal{S}_t$ at each of its points is $t$. If $\mathcal{S}_t$ is a $t$-semiarc in $\Pi_q$, $t<q$, then each line intersects $\mathcal{S}_t$ in at most $q+1-t$ points. Dover proved that semiovals (semiarcs with $t=1$) containing $q$ collinear points exist in $\Pi_q$ only if $q\leq 3$. We show that if $t>1$, then $t$-semiarcs with $q+1-t$ collinear points exist only if $t\geq \sqrt{q-1}$. In $\mathrm{PG}(2,q)$ we prove the lower bound $t\geq(q-1)/2$, with equality only if $\mathcal{S}_t$ is a blocking set of Rédei type of size $3(q+1)/2$.We call the symmetric difference of two lines, with $t$ further points removed from each line, a $V_t$-configuration. We give conditions ensuring a $t$-semiarc to contain a $V_t$-configuration and give the complete characterization of such $t$-semiarcs in $\mathrm{PG}(2,q)$.

NONDETERMINISTIC STATE COMPLEXITY OF PROPORTIONAL REMOVALS

2014 ◽  
Vol 25 (07) ◽  
pp. 823-835 ◽  
Author(s):  
DANIEL GOČ ◽  
ALEXANDROS PALIOUDAKIS ◽  
KAI SALOMAA
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
State Complexity ◽  
Nondeterministic State

The language [Formula: see text] consists of first halfs of strings in L. Many other variants of a proportional removal operation have been considered in the literature and a characterization of removal operations that preserve regularity is known. We consider the nondeterministic state complexity of the operation [Formula: see text] and, more generally, of polynomial removals as defined by Domaratzki (J. Automata, Languages and Combinatorics 7(4), 2002). We give an O(n2) upper bound for the nondeterministic state complexity of polynomial removals and a matching lower bound in cases where the polynomial is a sum of a monomial and a constant, or when the polynomial has rational roots.

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