منابع مشابه
Path decompositions of regular graphs with prescribed girth
A P -decomposition of a graph G is a set of pairwise edge-disjoint paths of G with edges that cover the edge set of G. Kotzig (1957) proved that a 3-regular graph admits a P3-decomposition if and only if it contains a perfect matching, and also asked what are the necessary and sufficient conditions for an -regular graph to admit a P -decomposition, for odd . Let g, and m be positive integers wi...
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Let us denote by EX (m,n; {C4, . . . , C2t}) the family of bipartite graphs G with m and n vertices in its classes that contain no cycles of length less than or equal to 2t and have maximum size. In this paper the following question is proposed: does always such an extremal graph G contain a (2t + 2)-cycle? The answer is shown to be affirmative for t = 2, 3 or whenever m and n are large enough ...
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We give an upper bound for the online chromatic number of graphs with high girth and for graphs with high oddgirth generalizing Kierstead’s algorithm for graphs that contain neither a C3 or C5 as an induced subgraph. keywords: online algorithms, combinatorial problems
متن کاملRegular Graphs of given Girth
Graph theory is the study of mathematical structures called graphs. We define a graph as a pair (V,E), where V is a nonempty set, and E is a set of unordered pairs of elements of V . V is called the set of vertices of G, and E is the set of edges. Two vertices a and b are adjacent provided (a, b) ∈ E. If a pair of vertices is adjacent, the vertices are referred to as neighbors. We can represent...
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We say that a bipartite graph Γ(V1 ∪ V2, E) has bi-degree r, s if every vertex from V1 has degree r and every vertex from V2 has degree s. Γ is called an (r, s, t)–graph if, additionally, the girth of Γ is 2t. For t > 3, very few examples of (r, s, t)–graphs were previously known. In this paper we give a recursive construction of (r, s, t)–graphs for all r, s, t ≥ 2, as well as an algebraic con...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1994
ISSN: 0095-8956
DOI: 10.1006/jctb.1994.1015