scholarly journals On Lower Bounds for the Matching Number of Subcubic Graphs

2016 ◽  
Vol 85 (2) ◽  
pp. 336-348 ◽  
Author(s):  
P. E. Haxell ◽  
A. D. Scott
Keyword(s):  
Lower Bounds ◽  
Matching Number ◽  
Subcubic Graphs

Lower bounds of graph energy in terms of matching number

2018 ◽  
Vol 549 ◽  
pp. 276-286 ◽  
Author(s):  
Dein Wong ◽  
Xinlei Wang ◽  
Rui Chu
Keyword(s):  
Lower Bounds ◽  
Matching Number ◽  
Graph Energy

scholarly journals Tight lower bounds on the matching number in a graph with given maximum degree

2018 ◽  
Vol 89 (2) ◽  
pp. 115-149 ◽  
Author(s):  
Michael A. Henning ◽  
Anders Yeo
Keyword(s):  
Lower Bounds ◽  
Maximum Degree ◽  
Matching Number

Interval Packing and Covering in the Boolean Lattice

1996 ◽  
Vol 5 (4) ◽  
pp. 373-384 ◽  
Author(s):  
Konrad Engel
Keyword(s):  
Lower Bounds ◽  
Pairwise Disjoint ◽  
Boolean Lattice ◽  
Covering Number ◽  
Matching Number ◽  
Packing And Covering ◽  
Minimum Number ◽  
Fractional Numbers

Let be the hypergraph whose points are the subsets X of [n] := {1,…,n} with l≤ |X| ≤ u, l < u, and whose edges are intervals in the Boolean lattice of the form I = {C ⊆[n] : X⊆C⊆Y} where |X| = l, |Y| = u, X ⊆ Y.We study the matching number i.e. the the maximum number of pairwise disjoint edges, and the covering number i.e. the minimum number of points which cover all edges. We prove that max and that for every ε > 0 the inequalities hold, where for the lower bounds we suppose that n is not too small. The corresponding fractional numbers can be determined exactly. Moreover, we show by construction that

Lower Bounds on the Uniquely Restricted Matching Number

2019 ◽  
Vol 35 (1) ◽  
pp. 353-361 ◽  
Author(s):  
M. Fürst ◽  
D. Rautenbach
Keyword(s):  
Lower Bounds ◽  
Matching Number

scholarly journals From Edge-Coloring to Strong Edge-Coloring

10.37236/3529 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Valentin Borozan ◽  
Gerard Jennhwa Chang ◽  
Nathann Cohen ◽  
Shinya Fujita ◽  
Narayanan Narayanan ◽  
...  
Keyword(s):  
Set Theory ◽  
Lower Bounds ◽  
Edge Coloring ◽  
Upper And Lower Bounds ◽  
Combinatorial Set ◽  
Proper Edge Coloring ◽  
Complete Bipartite Graphs ◽  
Np Complete ◽  
Subcubic Graphs ◽  
Combinatorial Set Theory

In this paper we study a generalization of both proper edge-coloring and strong edge-coloring: $k$-intersection edge-coloring, introduced by Muthu, Narayanan and Subramanian. In this coloring, the set $S(v)$ of colors used by edges incident to a vertex $v$ does not intersect $S(u)$ on more than $k$ colors when $u$ and $v$ are adjacent. We provide some sharp upper and lower bounds for $\chi'_{k\text{-int}}$ for several classes of graphs. For $l$-degenerate graphs we prove that $\chi'_{k\text{-int}}(G)\leq (l+1)\Delta -l(k-1)-1$. We improve this bound for subcubic graphs by showing that $\chi'_{2\text{-int}}(G)\leq 6$. We show that calculating $\chi'_{k\text{-int}}(K_n)$ for arbitrary values of $k$ and $n$ is related to some problems in combinatorial set theory and we provide bounds that are tight for infinitely many values of $n$. Furthermore, for complete bipartite graphs we prove that $\chi'_{k\text{-int}}(K_{n,m}) = \left\lceil \frac{mn}{k}\right\rceil$. Finally, we show that computing $\chi'_{k\text{-int}}(G)$ is NP-complete for every $k\geq 1$.An addendum was added to this paper on Jul 4, 2015.

scholarly journals Sharp lower bounds on the fractional matching number

2015 ◽  
Vol 186 ◽  
pp. 272-274 ◽  
Author(s):  
Roger E. Behrend ◽  
Suil O ◽  
Douglas B. West
Keyword(s):  
Lower Bounds ◽  
Matching Number

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
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