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Graphs with Linearly Bounded Ramsey Numbers
TLDR
We prove that a graph G of order n is p -arrangeable if its vertices can be ordered as v 1 , v 2 , ..., v n such that | N L i ( N Ri ( v i ))| ≤ p for each 1 ≤ i ≤ n − 1, where L i denotes the vertices of the graph and R i denotes its neighbors. Expand
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A generalization of Fan's condition for Hamiltonicity, pancyclicity, and Hamiltonian connectedness
TLDR
A weakened version of Fan's condition for Hamiltonicity is sufficient for a 2-connected graph to be pancyclic (with a few exceptions). Expand
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Second Neighborhood via First Neighborhood in Digraphs
Abstract. Let D be a simple digraph without loops or digons. For any $ v\in V(D) $, the first out-neighborhood N+(v) is the set of all vertices with out-distance 1 from v and the second neighborhoodExpand
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An Interlacing Result on Normalized Laplacians
TLDR
Cauchy interlacing-type properties of the normalized Laplacian associated with the graph G, denoted ${\cal L}(G), are investigated, and the following result is established. Expand
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Saturation numbers for families of Ramsey-minimal graphs
Given a family of graphs F , a graph G is F-saturated if no element of F is a subgraph of G, but for any edge e in G, some element of F is a subgraph of G + e. Let sat(n,F) denote the minimum numberExpand
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Graphs with a Cycle of Length Divisible by Three
TLDR
In this paper, we prove that every graph G with minimum degree G contains a cycle of length divisible by three. Expand
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Homeomorphically irreducible spanning trees
TLDR
We show that if G is a graph such that every edge is in at least two triangles, then G contains a spanning tree with no vertex of degree 2 (a homeomorphically irreducible spanning tree). Expand
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Around a biclique cover conjecture
We address an old (1977) conjecture of a subset of the authors (a variant of Ryser's conjecture): in every r-coloring of the edges of a biclique [A,B] (complete bipartite graph), the vertex set canExpand
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Ramsey Problems Involving Degrees in Edge-colored Complete Graphs of Vertices Belonging to Monochromatic Subgraphs
TLDR
We consider monochromatic subragraphs in two-colored graphs as guaranteed by Ramsey's theorem, and ask various questions concerning the degree in the two- colored complete graphs of vertices which are part of these subgraphs. Expand
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Transforming Complete Coverage Algorithms to Partial Coverage Algorithms for Wireless Sensor Networks
TLDR
In this work, we propose a framework with strategies that can transform almost any existing complete coverage algorithm with any coverage ratio to an algorithm that can -cover the area to trade for network lifetime. Expand
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