Graphs and Combinatorics (GRAPH COMBINATOR )

Publisher: Springer Verlag


Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers and survey articles the journal also features short communications research problems and announcements. As particular attention is being paid to rapid publication researchers not only rely on Graphs and Combinatorics to keep them informed of current developments but also use it as a forum for publicizing their own work. Graphs and Combinatorics covers: graph theory combinatorics

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  • Website
    Graphs and Combinatorics website
  • Other titles
    Graphs and combinatorics (Online), Graphs & combinatorics
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  • Material type
    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

Publisher details

Springer Verlag

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    • Author can archive a pre-print version
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    • Author can archive a post-print version
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    • Authors own final version only can be archived
    • Publisher's version/PDF cannot be used
    • On author's website or institutional repository
    • On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
    • Published source must be acknowledged
    • Must link to publisher version
    • Set phrase to accompany link to published version (The original publication is available at
    • Articles in some journals can be made Open Access on payment of additional charge
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Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper we obtain criteria which allow us to decide, for a large class of graphs, whether they are hyperbolic or not. We are especially interested in the planar graphs which are the ``boundary" (the $1$-skeleton) of a tessellation of the Euclidean plane. Furthermore, we prove that a graph obtained as the $1$-skeleton of a general CW $2$-complex is hyperbolic if and only if its dual graph is hyperbolic.
    Graphs and Combinatorics 01/2015;
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    ABSTRACT: Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005) showed that every 3-connected N 2-locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of G is Hamiltonian. It is best possible in some sense.
    Graphs and Combinatorics 09/2014; 30(5).
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    ABSTRACT: In this paper, we present a sharp upper bound for the least signless Laplacian eigenvalue of a graph involving its domination number. Moreover, we determine some extremal graphs which attain the sharp bound.
    Graphs and Combinatorics 09/2014;
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    ABSTRACT: We consider only digraphs that are oriented graphs, meaning orientations of simple finite graphs. An oriented graph $D=(V,A)$ with minimum degree $d$ is called $d$-arc-dominated if for every arc $(x,y) \in A$ there is a vertex $u \in V$ with outdegree $d$ such that both $(u,x) \in A$ and $(u,y) \in A$ hold. In this paper, we show that for any integer $d \ge 3$ the girth of a $d$-arc-dominated oriented graph is less than or equal to $d$. Moreover, for every integer $t$ with $3 \le t \le d$ there is a $d$-arc-dominated oriented graph with girth $t$. We also give a characterization for oriented graphs with both minimum outdegree and girth $d$ to be $d$-arc-dominated and classify all $d$-arc-dominated $d$-circular oriented graphs with girth $d$.
    Graphs and Combinatorics 07/2014; 30(4):1045 - 1054.
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    ABSTRACT: The automorphic H-chromatic index of a graph Γ is the minimum integer m for which Γ has a proper edge-coloring with m colors preserved by a given subgroup H of the full automorphism group of Γ. We determine upper bounds for this index in terms of the chromatic index of Γ for some abelian 2-groups H.
    Graphs and Combinatorics 07/2014;
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    ABSTRACT: The square $G^2$ of a graph $G$ is defined on the vertex set $V(G)$ of $G$ such that any two vertices with distance at most two in $G$ are linked by an edge. In this paper, the chromatic number and equitable chromatic number of the square $S^2(n,k)$ of Sierpiński graph $S(n,k)$ are studied. It is obtained that $\chi (S^2(n,k))=\chi _{=}(S^2(n,k))=k+1$ for $n\ge 2$ and $k\ge 2$ .
    Graphs and Combinatorics 06/2014;
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    ABSTRACT: Let k be a non-negative integer. A branch vertex of a tree is a vertex of degree at least three. We show two sufficient conditions for a connected claw-free graph to have a spanning tree with a bounded number of branch vertices: (i) A connected claw-free graph has a spanning tree with at most k branch vertices if its independence number is at most 2k + 2. (ii) A connected claw-free graph of order n has a spanning tree with at most one branch vertex if the degree sum of any five independent vertices is at least n − 2. These conditions are best possible. A related conjecture also is proposed.
    Graphs and Combinatorics 03/2014;
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    ABSTRACT: A vertex is simplicial if the vertices of its neighborhood are pairwise adjacent. It is known that, for every vertex v of a chordal graph, there exists a simplicial vertex among the vertices at maximum distance from v. Here we prove similar properties in other classes of graphs related to that of chordal graphs. Those properties will not be in terms of simplicial vertices, but in terms of other types of vertices that are used to characterize those classes.
    Graphs and Combinatorics 01/2014;
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    ABSTRACT: A proper t-coloring of a graph G is a mapping ${\varphi: V(G) \rightarrow [1, t]}$ such that ${\varphi(u) \neq \varphi(v)}$ if u and v are adjacent vertices, where t is a positive integer. The chromatic number of a graph G, denoted by ${\chi(G)}$ , is the minimum number of colors required in any proper coloring of G. A linear t-coloring of a graph is a proper t-coloring such that the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number of a graph G, denoted by ${lc(G)}$ , is the minimum t such that G has a linear t-coloring. In this paper, the linear t-colorings of Sierpiński-like graphs S(n, k), ${S^+(n, k)}$ and ${S^{++}(n, k)}$ are studied. It is obtained that ${lc(S(n, k))= \chi (S(n, k)) = k}$ for any positive integers n and k, ${lc(S^+(n, k)) = \chi(S^+(n, k)) = k}$ and ${lc(S^{++}(n, k)) = \chi(S^{++}(n, k)) = k}$ for any positive integers ${n \geq 2}$ and ${k \geq 3}$ . Furthermore, we have determined the number of paths and the length of each path in the subgraph induced by the union of any two color classes completely.
    Graphs and Combinatorics 01/2014;
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    ABSTRACT: The Cycle Double Cover Conjecture claims that every bridgeless graph has a cycle double cover and the Strong Cycle Double Conjecture states that every such graph has a cycle double cover containing any specified circuit. In this paper, we get a necessary and sufficient condition for bridgeless graphs to have a strong 5-cycle double cover. Similar condition for the existence of 5-cycle double covers is also obtained. These conditions strengthen/improve some known results.
    Graphs and Combinatorics 01/2014;
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    ABSTRACT: We obtain two identities and an explicit formula for the number of homomorphisms of a finite path into a finite path. For the number of endomorphisms of a finite path these give over-count and under-count identities yielding the closed-form formulae of Myers. We also derive finite Laurent series as generating functions which count homomorphisms of a finite path into any path, finite or infinite.
    Graphs and Combinatorics 01/2014;
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    ABSTRACT: For a connected graph G = (V, E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x − y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A connected monophonic set of G is a monophonic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected monophonic set of G is the connected monophonic number of G and is denoted by m c (G). We determine bounds for it and characterize graphs which realize these bounds. For any two vertices u and v in G, the monophonic distance d m (u, v) from u to v is defined as the length of a longest u − v monophonic path in G. The monophonic eccentricity e m (v) of a vertex v in G is the maximum monophonic distance from v to a vertex of G. The monophonic radius rad m G of G is the minimum monophonic eccentricity among the vertices of G, while the monophonic diameter diam m G of G is the maximum monophonic eccentricity among the vertices of G. It is shown that for positive integers r, d and n ≥ 5 with r < d, there exists a connected graph G with rad m G = r, diam m G = d and m c (G) = n. Also, if a,b and p are positive integers such that 2 ≤ a < b ≤ p, then there exists a connected graph G of order p, m(G) = a and m c (G) = b.
    Graphs and Combinatorics 01/2014;
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    ABSTRACT: The article shrinks the Δ = 6 hole that exists in the family of planar graphs which satisfy the total coloring conjecture. Let G be a planar graph. If ${v_n^k}$ represents the number of vertices of degree n which lie on k distinct 3-cycles, for ${n, k \in \mathbb{N}}$ , then the conjecture is true for planar graphs which satisfy ${v_5^4 +2(v_5^{5^+} +v_6^4) +3v_6^5 +4v_6^{6^+} < 24}$ .
    Graphs and Combinatorics 01/2014;
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    ABSTRACT: While the Steiner problem has been extensively studied in the Euclidean plane, it remains an open problem to solve the Steiner problem on arbitrary non-planar (piecewise smooth) surfaces. We suggest an algorithm for solving the n-point Steiner problem on surfaces of revolution which have a non-decreasing generating function by constructing an isometric framework on a plane endowed with a weighted distance metric, thus propelling a new analytical avenue for studying the Steiner problem on surfaces with non-constant curvature.
    Graphs and Combinatorics 01/2014;

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