Add to ORKGWe characterize the extremal trees that maximize the number of almost-perfect matchings, which are matchings covering all but one or two vertices, and those that maximize the number of strong almost-perfect matchings, which are matchings missing only one or two leaves. We also determine the trees that minimize the number of maximal matchings. We apply these results to extremal problems on the weighted Hosoya index for several choices of vertex-degree-based weight function.Comment: 21 pages, 8 figure
AbstractThe structural theory of matchings is used to establish lower bounds on the number of perfec...
AbstractPractical questions arising from (for instance) biological applications can often be express...
The greedy tree G(D) and the M-tree M(D) are known to be extremal among trees with degree sequence D...
AbstractForests on n vertices with maximum number of maximal matchings are called extremal forests. ...
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
AbstractWe determine upper and lower bounds for the number of maximum matchings (i.e., matchings of ...
This dissertation answers several questions in extremal graph theory, each concerning the maximum or...
Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed thatthe maximum anti-forcin...
Due to a classical result of Berge, it is known that a matching of any graph can be turned into a ma...
AbstractThe Hosoya index of a graph is defined as the total number of independent edge subsets of th...
An odd path packing in a graph is a collection of edge-disjoint odd length paths such that each node...
For a fixed graph $F$, a graph $G$ is said to be $F$-saturated if $G$ does not contain a subgraph is...
This dissertation answers several questions in extremal graph theory, each concerning the maximum or...
[3] have recently determined the maximum number of edges of a chordal graph with a maximum degree le...
Blair et. al. [3] have recently determined the maximum number of edges of a chordal graph with a max...
AbstractThe structural theory of matchings is used to establish lower bounds on the number of perfec...
AbstractPractical questions arising from (for instance) biological applications can often be express...
The greedy tree G(D) and the M-tree M(D) are known to be extremal among trees with degree sequence D...
AbstractForests on n vertices with maximum number of maximal matchings are called extremal forests. ...
We prove that there is $c>0$ such that for all sufficiently large $n$, if $T_1,\dots,T_n$ are any tr...
AbstractWe determine upper and lower bounds for the number of maximum matchings (i.e., matchings of ...
This dissertation answers several questions in extremal graph theory, each concerning the maximum or...
Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed thatthe maximum anti-forcin...
Due to a classical result of Berge, it is known that a matching of any graph can be turned into a ma...
AbstractThe Hosoya index of a graph is defined as the total number of independent edge subsets of th...
An odd path packing in a graph is a collection of edge-disjoint odd length paths such that each node...
For a fixed graph $F$, a graph $G$ is said to be $F$-saturated if $G$ does not contain a subgraph is...
This dissertation answers several questions in extremal graph theory, each concerning the maximum or...
[3] have recently determined the maximum number of edges of a chordal graph with a maximum degree le...
Blair et. al. [3] have recently determined the maximum number of edges of a chordal graph with a max...
AbstractThe structural theory of matchings is used to establish lower bounds on the number of perfec...
AbstractPractical questions arising from (for instance) biological applications can often be express...
The greedy tree G(D) and the M-tree M(D) are known to be extremal among trees with degree sequence D...