AbstractThe length of the shortest cycle in a graph G is called the girth of G. In particular, we show that if G has girth at least g and average degree at least d, then tw(G)=Ω(1g+1(d−1)⌊(g−1)/2⌋). In view of a famous conjecture regarding the existence of graphs with girth g, minimum degree δ and having at most c(δ−1)⌊(g−1)/2⌋ vertices (for some constant c), this lower bound seems to be almost tight (but for a multiplicative factor of g+1)
AbstractLet Gn,g denote the class of all connected graphs on n vertices with fixed girth g. We prove...
AbstractIn this paper, a lower bound on the maximum genus of a graph in terms of its girth is establ...
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies ...
AbstractThe length of the shortest cycle in a graph G is called the girth of G. In particular, we sh...
The girth of a graph G is the length of a shortest cycle in G. Dobson (1994, Ph.D. dissertation, Lou...
AbstractThe girth of a graph G is the length of a shortest cycle in G. Dobson (1994, Ph. D. disserta...
AbstractThis paper determines lower bounds on the number of different cycle lengths in a graph of gi...
AbstractDobson (1994) conjectured that if G is a graph with girth no less than 2t + 1 and minimum de...
We show that any n‐vertex extremal graph G without cycles of length at most k has girth exactly $k+1...
AbstractWe prove that every graph of girth at least 5 with minimum degree δ ⩾ k/2 contains every tre...
AbstractWe prove that every graph of minimum degree at least r and girth at least 186 contains a sub...
AbstractLet EX(ν;{C3,…,Cn}) denote the set of graphs G of order ν that contain no cycles of length l...
AbstractIt is shown that a graph of large girth and minimum degree at least 3 share many properties ...
AbstractDobson (1994) conjectured that if G is a graph with girth no less than 2t + 1 and minimum de...
AbstractIt is shown that a graph of large girth and minimum degree at least 3 share many properties ...
AbstractLet Gn,g denote the class of all connected graphs on n vertices with fixed girth g. We prove...
AbstractIn this paper, a lower bound on the maximum genus of a graph in terms of its girth is establ...
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies ...
AbstractThe length of the shortest cycle in a graph G is called the girth of G. In particular, we sh...
The girth of a graph G is the length of a shortest cycle in G. Dobson (1994, Ph.D. dissertation, Lou...
AbstractThe girth of a graph G is the length of a shortest cycle in G. Dobson (1994, Ph. D. disserta...
AbstractThis paper determines lower bounds on the number of different cycle lengths in a graph of gi...
AbstractDobson (1994) conjectured that if G is a graph with girth no less than 2t + 1 and minimum de...
We show that any n‐vertex extremal graph G without cycles of length at most k has girth exactly $k+1...
AbstractWe prove that every graph of girth at least 5 with minimum degree δ ⩾ k/2 contains every tre...
AbstractWe prove that every graph of minimum degree at least r and girth at least 186 contains a sub...
AbstractLet EX(ν;{C3,…,Cn}) denote the set of graphs G of order ν that contain no cycles of length l...
AbstractIt is shown that a graph of large girth and minimum degree at least 3 share many properties ...
AbstractDobson (1994) conjectured that if G is a graph with girth no less than 2t + 1 and minimum de...
AbstractIt is shown that a graph of large girth and minimum degree at least 3 share many properties ...
AbstractLet Gn,g denote the class of all connected graphs on n vertices with fixed girth g. We prove...
AbstractIn this paper, a lower bound on the maximum genus of a graph in terms of its girth is establ...
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies ...
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