Leaf realization problem, caterpillar graphs and prefix normal words

被引:6
|
作者
Masse, Alexandre Blondin [1 ]
de Carufel, Julien [2 ]
Goupil, Alain [2 ]
Lapointe, Melodie [1 ]
Nadeau, Emile [1 ]
Vandomme, Elise [1 ]
机构
[1] Univ Quebec Montreal, Lab Combinatoire & Informat Math, Montreal, PQ, Canada
[2] Univ Quebec Trois Rivieres, Lab Interdisciplinaire Rech Imagerie & Combinatoi, Trois Rivieres, PQ, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Graph theory; Combinatorics on words; Induced subtrees; Leaf; Prefix normal words; Prefix normal form; VERTICES;
D O I
10.1016/j.tcs.2018.04.019
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Given a simple graph G with n vertices and a natural number i n, let L-G(i) be the maximum number of leaves that can be realized by an induced subtree T of G with i vertices. We introduce a problem that we call the leaf realization problem, which consists in deciding whether, for a given sequence of n + 1 natural numbers (l(0), l(1),...,l(n)), there exists a simple graph G with n vertices such that l(i) = L-G(i) for i = 0,1,..., n. We present basic observations on the structure of these sequences for general graphs and trees. In the particular case where G is a caterpillar graph, we exhibit a bijection between the set of the discrete derivatives of the form (Delta L-G(i))(1 <= i <= n-3) and the set of prefix normal words. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:1 / 13
页数:13
相关论文
共 20 条
  • [1] On prefix normal words and prefix normal forms
    Burcsi, Peter
    Fici, Gabriele
    Liptak, Zsuzsanna
    Ruskey, Frank
    Sawada, Joe
    [J]. THEORETICAL COMPUTER SCIENCE, 2017, 659 : 1 - 13
  • [2] On Infinite Prefix Normal Words
    Cicalese, Ferdinando
    Liptak, Zsuzsanna
    Rossi, Massimiliano
    [J]. THEORY AND PRACTICE OF COMPUTER SCIENCE, SOFSEM 2019, 2019, 11376 : 122 - 135
  • [3] On infinite prefix normal words
    Cicalese, Ferdinando
    Liptak, Zsuzsanna
    Rossi, Massimiliano
    [J]. THEORETICAL COMPUTER SCIENCE, 2021, 859 : 134 - 148
  • [4] The asymptotic number of prefix normal words
    Balister, Paul
    Gerke, Stefanie
    [J]. THEORETICAL COMPUTER SCIENCE, 2019, 784 : 75 - 80
  • [5] On Combinatorial Generation of Prefix Normal Words
    Burcsi, Peter
    Fici, Gabriele
    Liptak, Zsuzsanna
    Ruskey, Frank
    Sawada, Joe
    [J]. COMBINATORIAL PATTERN MATCHING, CPM 2014, 2014, 8486 : 60 - 69
  • [6] Weighted Prefix Normal Words: Mind the Gap
    Eikmeier, Yannik
    Fleischmann, Pamela
    Kulczynski, Mitja
    Nowotka, Dirk
    [J]. DEVELOPMENTS IN LANGUAGE THEORY, DLT 2021, 2021, 12811 : 143 - 154
  • [7] A note on the longest common compatible prefix problem for partial words
    Crochemore, M.
    Iliopoulos, C. S.
    Kociumaka, T.
    Kubica, M.
    Langiu, A.
    Radoszewski, J.
    Rytter, W.
    Szreder, B.
    Walen, T.
    [J]. JOURNAL OF DISCRETE ALGORITHMS, 2015, 34 : 49 - 53
  • [8] Bubble-Flip-A New Generation Algorithm for Prefix Normal Words
    Cicalese, Ferdinando
    Liptak, Zsuzsanna
    Rossi, Massimiliano
    [J]. LANGUAGE AND AUTOMATA THEORY AND APPLICATIONS (LATA 2018), 2018, 10792 : 207 - 219
  • [9] Bubble-Flip-A new generation algorithm for prefix normal words
    Cicalese, Ferdinando
    Liptak, Zsuzsanna
    Rossi, Massimiliano
    [J]. THEORETICAL COMPUTER SCIENCE, 2018, 743 : 38 - 52
  • [10] Combinatorial Modifications of Reeb Graphs and the Realization Problem
    Michalak, Lukasz Patryk
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2021, 65 (04) : 1038 - 1060